Ultrasonic transducers

Ultrasonic transducers

ULTRASONIC TRANSDUCERS 2. Underwater sound transducers R. S. Woollett U l t r a s o n i c t r a n s d u c e r s a r e useful u n d e r w a t e r only...

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ULTRASONIC TRANSDUCERS 2. Underwater sound transducers R. S. Woollett

U l t r a s o n i c t r a n s d u c e r s a r e useful u n d e r w a t e r only when s h o r t r a n g e s a r e acceptable, but t h e i r s m a l l s i z e m a k e s t h e m convenient and allows use of g e n e r o u s s a f e t y f a c t o r s in d e s i g n . When r a n g e s of m o r e than a few k i l o m e t r e s a r e r e q u i r e d it i s n e c e s s a r y to move to the a u d i o - f r e q u e n c y range. The t r a n s d u c e r s then b e c o m e l a r g e and heavy, and the d e s i g n e r m u s t use m o r e s o p h i s t i c a t e d m e t h o d s to keep weight

U n d e r w a t e r sound t r a n s d u c e r s e x i s t in v a r i e t i e s e n c o m p a s s i n g f r e q u e n c i e s f r o m 1Hz to 10MHz, p o w e r s f r o m m i l l i w a t t s to m e g a w a t t s , and weights f r o m f r a c t i o n s of a k i l o g r a m to 100, 000 k i l o g r a m s o r m o r e . While s o m e a r e r e q u i r e d to work only a m e t r e o r two below the s u r f a c e , o t h e r s m u c h o p e r a t e at full o c e a n depths, w h e r e the s t a t i c p r e s s u r e may r e a c h 108 Nm - 2 . The s i z e and weight of t r a n s d u c e r s depend p r i m a r i l y on the o p e r a t i n g f r e q u e n c y and the p o w e r that they m u s t t r a n s m i t a s p r o j e c t o r s . The t r a n s d u c e r s u s e d a s p r o j e c t o r s usually s e r v e also a s r e c e i v e r s ; however, if the sole function of a t r a n s d u c e r is to r e c e i v e , then it is usually m u c h s m a l l e r and l i g h t e r .

and cost from becoming prohibitive. Problems that are currently challenging designers include adapting transducers to withstand ocean bottom pressures, determining more precisely the power limits of piezoelectric ceramics, and developing more powerful mathematical methods for array design.

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Attenuation

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In choosing an o p e r a t i n g frequency f o r an u n d e r w a t e r sound s y s t e m , one m u s t f i r s t c o n s i d e r the attenuation c h a r a c t e r i s t i c s of the ocean. The a v e r a g e attenuation of a nond i v e r g i n g wave is shown a s a function of f r e q u e n c y in F i g 1.1 F r o m the rapid i n c r e a s e of attenuation coefficient with f r e quency we may conclude that a s a t r a n s m i s s i o n channel the s e a w a t e r has l o w - p a s s c h a r a c t e r i s t i c s , with a h i g h - f r e q u e n c y r o l l - o f f rate that i n c r e a s e s with range. In addition to the attenuation shown in F i g 1, signal intensity is l o s t through s p h e r i c a l s p r e a d i n g at s h o r t r a n g e s and through c y l i n d r i c a l s p r e a d i n g at long r a n g e s , w h e r e the signal is confined bet w e e n h o r i z o n t a l l a y e r s . 2 T h e s e l o s s e s a r e independent of frequency.

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The p r a c t i c a l r e s u l t s of the s e a w a t e r ' s a c o u s t i c a l c h a r a c t e r i s t i c s a r e that 1MHz s i g n a l s a r e l i m i t e d to r a n g e s of t e n s of m e t r e s w h e r e a s at low audio f r e q u e n c i e s r a n g e s of thousands of k i l o m e t r e s a r e p o s s i b l e . U n d e r w a t e r sound applications fall into two main c a t e g o r i e s : c o m m u n i c a t i o n s , and echo ranging (in which a s c a t t e r i n g object f o r m s p a r t of the t r a n s m i s s i o n channel). In echo ranging the s ~ e of the t a r g e t influences the choice of f r e quency, s i n c e / n o r m a l l y one wants the sound wavelength to be s m a l l e r than the t a r g e t d i m e n s i o n s . D r Ralph S. Woollett, Navy U n d e r w a t e r Sound L a b o r a t o r y , New London, Connecticut 06320, USA

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Fig 1 Attenuation of non-diverging sound waves in seawater (s.ql|nity S5 parts per thousand, 5°C).

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Since d i r e c t i v i t y r e q u i r e m e n t s can be m e t with s m a l l - s i z e t r a n s d u c e r s at high f r e q u e n c i e s , high f r e q u e n c i e s a r e naturally to be p r e f e r r e d if the attenuation can be accepted. On the o t h e r hand, going to low f r e q u e n c i e s not only a f f o r d s lower attenuation but f a c i l i t a t e s radiation of higher p o w e r b e c a u s e of the l a r g e r radiating a r e a of the l o w - f r e q u e n c y transducers. P r o b a b l y the m o s t challenging_problem the t r a n s d u c e r d e s i g n e r has to face is developing t r a n s d u c e r s whose dynamic c h a r a c t e r i s t i c s will not be affected by ambient p r e s s u r e s up to 108 Nm -2 (1000 atm). In u n d e r w a t e r sound t r a n s d u c e r s , as in o t h e r e n g i n e e r i n g a r e a s , a l m o s t anything is p o s s i b l e if no c o n s t r a i n t s a r e placed on size, weight, and cost. At high f r e q u e n c i e s the t r a n s d u c e r s a r e naturally small; so the r e s t r i c t i o n s on s i z e and weight tend to be l i b e r a l and the d e s i g n e r can be g e n e r o u s in his use of m a t e r i a l s . L o w - f r e quency t r a n s d u c e r s , however, b e c o m e so l a r g e that s t r e n u o u s e f f o r t s m u s t be made to r e d u c e weight and c o s t s . So g r e a t e r ingenuity and m o r e exact t h e o r i e s a r e needed. The diff e r e n c e is analogous to that between designing land v e h i c l e s , w h e r e l a r g e safety f a c t o r s may be used, and d e s i g n i n g a i r craft, w h e r e the d e s i g n has to be r e f i n e d to e l i m i n a t e e v e r y surplus kilogram.

Ambient n o i s e Ambient n o i s e is a b a s i c c h a r a c t e r i s t i c of the ocean r e l e v a n t to the d e s i g n of r e c e i v i n g s y s t e m s . Fig 2 shows m i n i m u m l e v e l s of ambient n o i s e plotted v e r s u s f r e q u e n c y . Above 40kHz the m i n i m u m w a t e r n o i s e is f r o m t h e r m a l agitation of the w a t e r m o l e c u l e s , but below t h i s f r e q u e n c y e x c e s s noise e x i s t s even in calm s e a s . The p r e s e n c e of the e x c e s s n o i s e m a k e s life e a s i e r for the d e s i g n e r of a u d i o - f r e q u e n c y h y d r o phones. He can use n o n - r e s o n a n t h y d r o p h o n e s c o v e r i n g m u l t i - o c t a v e f r e q u e n c y r a n g e s and still keep his s y s t e m noise below m i n i m u m w a t e r n o i s e . In the h i g h - f r e q u e n c y range, w h e r e the l i m i t on absolute s e n s i t i v i t y is t h e r m a l noise, such bandwidths a r e not p o s s i b l e if the s y s t e m is r e q u i r e d to detect weak s i g n a l s . The d e s i r e d d i r e c t i v i t y patt e r n is of f i r s t i m p o r t a n c e when choosing a t r a n s d u c e r configuration. C o m m o n t y p e s of d i r e c t i v i t y p a t t e r n s a r e l i s t e d in Table 1, along with t r a n s d u c e r or a r r a y c o n f i g u r a t i o n s that a r e capable of producing the p a t t e r n s . Specific i l l u s t r a t i o n s of many of the l i s t e d t r a n s d u c e r s will be given in the following s e c t i o n s . At high f r e q u e n c i e s b e a m s t e e r i n g by m e c h a n i c a l rotation of the a r r a y is u s e d a g r e a t deal. A m o r e v e r s a t i l e s y s t e m is the s t a t i o n a r y m u l t i e l e m e n t a r r a y in which b e a m s t e e r i n g is a c c o m p l i s h e d e l e c t r o n i c a l l y by d i f f e r e n t i a l t i m e delay of the s i g n a l s feeding the t r a n s d u c e r e l e m e n t s . If the a r r a y c o v e r s a curved s u r f a c e , an a p e r t u r e may be f o r m e d by -dsing

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F i g 2 Minimum w a t e r n o i s e . Sea s t a t e 0 line (calm sen) s h o w s w e l l known Knudsen ambient n o i s e data, an e s t a b l i s h e d adequate p r a c t i c a l guide. The Wenz data3 s h o w s l o w e s t o b s e r v e d n o i s e under t y p i c a l l y quiet conditions. 244

ULTRASONICS October 1970

E l e c t r o n i c b e a m f o r m i n g and s t e e r i n g p e r m i t rapid scanning with l a r g e a r r a y s that could not be r o t a t e d at a rapid r a t e m e c h a n i c a l l y . T h e r e a r e o t h e r advantages to t h e s e t e c h niques. 4 In the r e c e i v i n g mode many d i f f e r e n t b e a m s can be f o r m e d s i m u l t a n e o u s l y and r o t a t e d independently. Adaptive b e a m f o r m i n g may be u s e d to d i s c r i m i n a t e against i n t e r f e r i n g n o i s e s a r r i v i n g f r o m d i s c r e t e d i r e c t i o n s . Shading of the a p e r t u r e function to r e d u c e s i d e - l o b e l e v e l s is e a s i l y controlled. ULTRASONIC TRANSDUCERS U l t r a s o n i c t r a n s d u c e r s a r e used in applications w h e r e only s h o r t r a n g e s a r e r e q u i r e d o r w h e r e high r e s o l u t i o n of s m a l l r e f l e c t i n g o b j e c t s is a n e c e s s i t y . Most c o m m e r c i a l applications of u n d e r w a t e r sound fall in t h e s e c a t e g o r i e s . Naval r e q u i r e m e n t s also e x i s t for s h o r t - r a n g e d e t e c t i o n of r e l a tively s m a l l o b j e c t s such a s m i n e s o r t o r p e d o e s . Some applications of u n d e r w a t e r sound that c o m m o n l y use f r e q u e n c i e s in the u l t r a s o n i c r a n g e include the following: Underwater telemetry. U n d e r w a t e r r e m o t e control, such a s anchor r e l e a s e systems. Dynamic ship positioning c o n t r o l s y s t e m s , for deep d r i l ling o p e r a t i o n s . Doppler navigation. B e a c o n s and t r a n s p o n d e r s , for p r e c i s i o n navigation in a predetermined area. Depth s o u n d e r s , o r f a t h o m e t e r s . S h o r t - r a n g e s o n a r for f i s h finding o r g e n e r a l s e a r c h i n g operations. S i d e - s c a n s o n a r for s e a f l o o r s u r v e y i n g . Acoustic imaging and a c o u s t i c holography. O c e a n o g r a p h i c i n s t r u m e n t a t i o n : wave height i n d i c a t o r s , c u r r e n t velocity m e t e r s , sound velocity m e t e r s . Some u l t r a s o n i c s o n a r s y s t e m s use pulse modulation and s o m e u s e continuous t r a n s m i s s i o n f r e q u e n c y modulation (CTFM). The insonifying s i g n a l s for a c o u s t i c imaging and a c o u s t i c holography, on the o t h e r hand, a r e u s u a l l y s i n g l e f r e q u e n c y CW. The t e r m 'acoustic i m a g i n g ' r e f e r s to a s y s t e m that u s e s a l e n s to f o r m an a c o u s t i c image; the image is c o n v e r t e d to e l e c t r i c a l s i g n a l s by m e t h o d s analogous to t h o s e u s e d in a t e l e v i s i o n c a m e r a . Although imaging s y s t e m s have s h o r t r a n g e s , b e c a u s e t h e i r o p e r a t i n g f r e q u e n c i e s a r e in the m e g a h e r t z region, they o r o t h e r h i g h - r e s o l u t i o n s o n a r s y s t e m s a r e needed to s u p p l e m e n t u n d e r w a t e r t e l e v i s i o n . In m a n y u n d e r s e a o p e r a t i o n s the turbidity is so g r e a t that opt i c a l t e l e v i s i o n is u s e l e s s . An example of a t r a n s d u c e r f o r the high u l t r a s o n i c range is shown in Fig 3. This t r a n s d u c e r p r o d u c e s a s e a r c h l i g h t b e a m when all the active e l e m e n t s a r e u s e d and two o r thogonal fan b e a m s when only the e l e m e n t s on the i n t e r s e c t i n g line s e c t i o n s (the c r o s s visible in the photograph) a r e u s e d . The t r a n s d u c e r c o n s i s t s of a m o s a i c of b a r i u m titanate p i e z o e l e c t r i c c e r a m i c p l a t e s which a r e r e s o n a n t in the t h i c k n e s s mode; that is, the t h i c k n e s s d i m e n s i o n of the p l a t e s is o n e - h a l f wavelength at the c e n t r e f r e q u e n c y of the 250-300MHz band.

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switching to s e l e c t a patch of e l e m e n t s facing in the d e s i r e d d i r e c t i o n . Then, by p r o p e r a d j u s t m e n t of the t i m e , d e l a y (o~' phasing in a n a r r o w - b a n d c a s e ) of each e l e m e n t to c o m p e n sate f o r the c u r v a t u r e , the a p e r t u r e is ' p h a s e d to a p l a n e . ' F u r t h e r a d j u s t m e n t of the t i m e d e l a y s allows the b e a m thus f o r m e d to be s t e e r e d in d i r e c t i o n .

The c e r a m i c p l a t e s a r e mounted on a l a y e r of c o r p r e n e , which is a ' p r e s s u r e - r e l e a s e ' m a t e r i a l , that is, a m a t e r i a l with low a c o u s t i c i m p e d a n c e . The c o r p r e n e i s o l a t e s the v i b r a t i n g p l a t e s f r o m the m e t a l housing and p r e v e n t s t h e i r r e a r s u r f a c e s f r o m radiating sound. Unfortunately, t h i s m a t e r i a l c o l l a p s e s at high h y d r o s t a t i c p r e s s u r e and l o s e s its p r e s s u r e - r e l e a s e q u a l i t i e s . T h e r e f o r e , t h i s t r a n s d u c e r i s l i m i t e d to d e p t h s of 200m. It was d e s i g n e d by A M E T E K / S t r a z a for u s e with a CTFM s o n a r f i s h c l a s s i f i e r .

Table 1 Radiators classified according to their directional patterns Omnidirectional (isotropic radiation) (a) Spherical shell, in radial vibration. Spherical array, driven in phase. ×

Small monopoles Double flexural-disk transducer. Flexural bars in b a r r e l - s t a v e configuration. Flextensional transducers. Miniaturized longitudinal vibrators.

a

Searchlight pattern (pencilbeam) (b)

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Plate, in thickness vibration. Plane array of single-ended transducers. Array on a curved surface, phased to a plane. Plane reflector plus plane array of monopoles or dipoles. Paraboloidal reflector (or lens) plus point source. Parabolic-cylinder reflector (or lens) plus line source. 3-dimensional array, phased to eliminate back lobe. Line array (along x-axis) phased for endfire.

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Toroidal pattern (horizontally omnidirectional) (c) Line array (along z-axis) driven in phase. Ring (in xy plane) in radial vibration, either capped or f r e e flooding. Pair of monopoles (along z-axis) with half-wave spacing.

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Fan pattern

(d)

Rectangular ar r ay (narrow in z-direction) of single-ended transducers; or line-fed parabolic-cylinder reflector or lens of similar aperature.

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Conical shell pattern (e) Phased line array (along z-axis).

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Dipole (f) Oscillating rigid body (shaker box). Edge-supported flexural disk radiating from both surfaces. Close-spaced antiphased monopole pair. Multtpole Multipole and cardioid patterns can be formed by proper combination of monopole sources. Multilobe patterns can also be produced by exciting the higher modes of common vibrators such as rings, spherical shells, and flexural disks.

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d i e l e c t r i c constant of the c e r a m i c s gives them an i m p o r t a n t advantage. F o r the s a m e a c o u s t i c power, the e l e c t r i c field in the m a t e r i a l and the voltage on the cable can be much l o w e r when the p i e z o e l e c t r i c c e r a m i c s a r e u s e d . The higher s t r e n g t h of the c e r a m i c s was also i m p o r t a n t in helping t h e m d i s p l a c e the w a t e r - s o l u b l e c r y s t a l s such a s ADP. A l a r g e r longitudinal v i b r a t o r suitable for the l o w e r u l t r a sonic range is shown in F i g 5. The active portion c o n s i s t s of two lead z i r c o n a t e titanate rings, i n t e r p o s e d between an aluminum radiating head and a s t e e l tail s e c t i o n . The r e s o n a t o r s o p e r a t e in o i l - f i l l e d housings. P r e s t r e s s i n g of the c e r a m i c allows pulse i n t e n s i t i e s up to 10Wcm -2 to be achieved. The t r a n s d u c e r a s s e m b l y shown in Fig 6 is r e p r e s e n t a t i v e of c u r r e n t p r a c t i c e in the m e d i u m u l t r a s o n i c range, w h e r e r u b b e r windows have sufficiently low l o s s and p r o v i d e a v e r y p r a c t i c a l method of e n c l o s u r e . The bottom t r a n s d u c e r is the one p r e v i o u s l y shown in Fig 4; in this a s s e m b l y , designed for the A M E T E K / S t r a z a Model 500 CTFM sonar, it is

Fig 3 A m o s a i c t r a n s d u c e r for the 2 5 0 - 3 0 0 M H z range. The c e r a m i c s t r u c t u r e i s shown p r i o r to the putting o p e r a tion in which it i s c o v e r e d with s i l i c o n e rubber.

The acoustic isolation p r o b l e m mentioned above o c c u r s v e r y often in t r a n s d u c e r work. Usually c e r t a i n s u r f a c e s of the basic v i b r a t o r have to be shielded a c o u s t i c a l l y f r o m the water; o t h e r w i s e the radiation f r o m t h e s e s u r f a c e s will c o m bine with that f r o m the m a i n r a d i a t i n g s u r f a c e in a way that is h a r m f u l to the radiation p a t t e r n o r to the a c o u s t i c loading of the t r a n s d u c e r . P r e s s u r e - r e l e a s e m a t e r i a l s provide a s a t i s f a c t o r y solution to the isolation p r o b l e m only at m o d e r a t e depths. A t r a n s d u c e r can be adapted f o r g r e a t depths if the s p a c e between the v i b r a t o r and the housing is filled with oil ins t e a d of p r e s s u r e - r e l e a s e m a t e r i a l . It is not obvious, howe v e r , that the oil will p r o v i d e decoupling s i n c e its s p e c i f i c a c o u s t i c i m p e d a n c e is l o w e r than that of the p i e z o e l e c t r i c c e r a m i c by only a f a c t o r of about 20. But if the m e t a l housing is m a d e sufficiently thick, the combination of the oil and the housing will provide high t r a n s m i s s i o n l o s s . At u l t r a s o n i c f r e q u e n c i e s the t r a n s d u c e r s a r e so s m a l l that the u s e of thick rigid housings d o e s not o r d i n a r i l y c a u s e a weight p r o b l e m and oil filling is t h e r e f o r e a v e r y s u c c e s s f u l t e c h nique. 5 Sea p r e s s u r e is c o m m u n i c a t e d to the oil r e s e r v o i r so that the t r a n s d u c e r ' s i n t e r n a l p r e s s u r e is equalized with its e x t e r n a l p r e s s u r e .

Fig 4 An a r r a y of longitudir~l v i b r a t o r s . At the c e n t r e frequency, h o r i z o n t a l beamwidth i s 2 . 5 °. A suba s s e m b l y of four t r a n s d u c e r e l e m e n t s i s shown in the foreground.

Fig 4 shows a t r a n s d u c e r that is d e s i g n e d to be o i l - f i l l e d and is usable at unlimited depths. It c o n s i s t s of an a r r a y of c o m posite longitudinal v i b r a t o r s and p r o d u c e s a f a n - t y p e b e a m . The a r r a y contains 132 individual t r a n s d u c e r s , but it is cons t r u c t e d in module f o r m with 4 t r a n s d u c e r s to a module. Each t r a n s d u c e r e l e m e n t c o n s i s t s of a lead z i r c o n a t e titanate c e r a m i c disk with m e t a l l i c head and tail m a s s e s . It was developed by A M E T E K / S t r a z a for use at 60-100kHz. This c o m p o s i t e type of longitudinal v i b r a t o r ( s o m e t i m e s called a 'tonpilz') p r o v i d e s a l o w e r r e s o n a n t f r e q u e n c y and a b r o a d e r bandwidth (lower m e c h a n i c a l - Q ) than the s t r a i g h t c e r a m i c type shown in Fig 3. Before p i e z o e l e c t r i c c e r a m i c s b e c a m e r e a d i l y available in about 1950, t r a n s d u c e r s such a s t h o s e shown in F i g s 3 and 4 would probably have been made of ADP c r y s t a l s . ADP h a s a n u m b e r of d e s i r a b l e p r o p e r t i e s , such as r e a s o n a b l y good e l e c t r o m e c h a n i c a l coupling (k = 0.28), low s p e c i f i c acoustic impedance, and excellent u n i f o r m i t y and f r e e d o m f r o m ageing e f f e c t s . The c o m p o s i t e s t r u c t u r e shown in F i g 4, whose use i m p r o v e s the impedance m a t c h of the c e r a m i c to the w a t e r , would not be needed if ADP c r y s t a l s w e r e u s e d . Since t h e i r s p e c i f i c a c o u s t i c i m p e d a n c e i s only about one q u a r t e r that of the c e r a m i c , the c r y s t a l s even in plain b a r f o r m a r e well loaded by the w a t e r . In spite of its good f e a t u r e s , ADP has b e e n a l m o s t e n t i r e l y s u p e r s e d e d by the p i e z o e l e c t r i c c e r a m i c s . The much higher 246

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F ~ 5 A longitudinal-vibrator t r a n s d u c e r developed by International T r a n s d u c e r Corp for the 13-20kHz range. The r e s o n a t o r i s 90ram lc~g and 57mm in d i a m e t e r . A tie rod through the c e n t r e puts a c o m p r e s s i v e b i a s of 3 x 107 N m - Z o n the c e r a m i c .

limit, o v e r a n a r r o w f r e q u e n c y band. If broadband nonr e s o n a n t hydrophones a r e used, the absolute sensitivity, r e l a t i v e to t h e r m a l noise, will n e c e s s a r i l y be low. Such hyd r o p h o n e s , however, have applications in l a b o r a t o r y tanks, and they may be m a d e r e m a r k a b l y s m a l l 8 and t h e r e f o r e useful a s p r o b e s at v e r y high f r e q u e n c i e s .

AUDIO-FREQUENCY TRANSDUCERS When Paul Langevin worked on the echo-ranging approach to submarine detection during World War I, he used ultrasonic frequencies. 9 In postwar naval developments the United States and Great Britain continued in this ultrasonic vein.

F i g 6 An u l t r a s o n i c t r a n s d u c e r a s s e m b l y showing watertight c o n s t r u c t i o n b a s e d on the u s e of rubber windows.

u s e d a s the r e c e i v e r . The t r a n s d u c e r at the top, which i s the p r o j e c t o r , c o n s i s t s of a v e r t i c a l line of 4 v i b r a t o r s , v e r y m u c h like the single module shown in the f o r e g r o u n d of F i g 4. This line a r r a y is set in a lead p l a n a r baffle and has a b e a m that is about 60 ° wide in the h o r i z o n t a l plane and 15 ° wide in the v e r t i c a l plane. In the s o n a r s y s t e m the a s s e m b l y is m e c h a n i c a l l y rotated, o s c i l l a t i n g up to 360 ° f o r wide c o v e r a g e o r o v e r a 15 ° s e c t o r f o r n a r r o w scan. O t h e r c e r a m i c s h a p e s a r e e m p l o y e d in addition to the s i m p l e o n e s u s e d in the longitudinal v i b r a t o r s . F o r o m n i d i r e c t i o n a l radiation, hollow c e r a m i c s p h e r e s v i b r a t i n g in the lowest c i r c u m f e r e n t i a l mode (uniform r a d i a l motion) a r e useful. C e r a m i c r i n g s v i b r a t i n g in t h e i r lowest mode (hoop mode) may be stacked in the axial d i r e c t i o n to f o r m a line s o u r c e , which gives a t o r o i d a l p a t t e r n . F o r f r e q u e n c i e s in the m e g a h e r t z range, single c e r a m i c p l a t e s r e s o n a n t in the t h i c k n e s s d i r e c t i o n a r e used, and they give s e a r c h l i g h t p a t t e r n s . P l a s t i c o r liquid l e n s e s a r e u s e d in conjunction with t r a n s d u c e r s to aid in b e a m f o r m i n g . R e f l e c t o r s and h o r n s a r e also f e a s i b l e . F o r a m e t a l r e f l e c t o r or horn to work u n d e r w a t e r it m u s t be m u c h t h i c k e r and h e a v i e r than s i m i l a r d e v i c e s u s e d in a i r . O t h e r w i s e the m e t a l i n t e r f a c e will not a p p r o x i m a t e a rigid boundary to the r e l a t i v e l y h i g h - i m pedance w a t e r m e d i u m . In u l t r a s o n i c s t h e s e d e v i c e s a r e s m a l l enough to be m a d e thick without t h e i r weight b e c o m i n g p r o h i b i t i v e . Even so, t h e r e m a y be f r e q u e n c i e s in the d e s i r e d band w h e r e n o r m a l m o d e s of the horn o r r e f l e c t o r a r e excited, and then the device b e c o m e s a s e c o n d a r y r a d i a t o r r a t h e r than a rigid waveguide. M a g n e t o s t r i c t i v e m e t a l s a r e no longer u s e d in u l t r a s o n i c t r a n s d u c e r s to any g r e a t extent, b e c a u s e t h e i r e d d y - c u r r e n t l o s s e s c a u s e low efficiency and thus make t h e m n o n c o m petitive with the p i e z o e l e c t r i c c e r a m i c s (though t h i s conclusion m a y be contested6). M a g n e t o s t r i c t i v e f e r r i t e s a r e devoid of eddy c u r r e n t s , but they have no significant adv a n t a g e s o v e r the p i e z o e l e c t r i c c e r a m i c s and have had little u s e in u n d e r w a t e r sound. In u l t r a s o n i c s y s t e m s the r e c e i v i n g hydrophone n o r m a l l y o p e r a t e s at m e c h a n i c a l r e s o n a n c e ; in m a n y s y s t e m s it is the s a m e t r a n s d u c e r that is u s e d as the p r o j e c t o r . Mellen has shown 7 that the n o i s e in the r e c e i v i n g s y s t e m will e x c e e d the t h e r m a l n o i s e of the w a t e r (which is the i r r e d u c i b l e l i m i t on w a t e r noise for f r e q u e n c i e s above about 40kHz) by the f a c t o r F/7/ea, w h e r e F is the n o i s e f a c t o r of the r e c e i v i n g a m p l i f i e r and ~ea is the t r a n s m i t t i n g efficiency of the r e c e i v i n g t r a n s d u c e r . Since r e s o n a n t t r a n s d u c e r s can be made with e f f i c i e n c y l o s s e s (10 log ~ ) of only 1 o r 2dB and the a m p l i f i e r noise f a c t o r can be kept below ldB if the t r a n s d u c e r is e l e c t r i c a l l y tuned, it is p o s s i b l e to have the r e c e i v ing s e n s i t i v i t y come within a few d e c i b e l s of the t h e r m a l

An advantage of this approach, which was important in securing acceptance for this new tactical tool, was that the transducer systems were small and could be added to naval vessels without requiring significant changes in hull design. After World War II, however, long-range surveillance, beyond the capability of the ultrasonic sonars, became a necessity. Hence navies were forced to develop audio-frequency sonar even though problems of increased difficulty had to be faced. In commercial underwater sound work, also, the shift to audio f r e q u e n c i e s m u s t be m a d e when r a n g e s of m o r e than a few k i l o m e t r e s a r e r e q u i r e d . U n d e r w a t e r telephony is an application of t h i s type; a c a r r i e r f r e q u e n c y of about 9kHz i s often u s e d . O c e a n o g r a p h i c r e s e a r c h in sound p r o p a g a t i o n of c o u r s e m u s t be conducted at low as well a s high f r e q u e n c i e s . If an u l t r a s o n i c t r a n s d u c e r s y s t e m is taken a s a prototype d e s i g n and a l o w - f r e q u e n c y t r a n s d u c e r s y s t e m is d e r i v e d f r o m it by l i n e a r scaling (all d i m e n s i o n s s c a l e d p r o p o r t i o n a l to the wavelength k), the weight will go up as k3. To keep the weight f r o m b e c o m i n g prohibitive the d e s i g n e r usually abandons s t r i c t scaling and t r i e s to e c o n o m i z e in his use of m a t e r i a l s . U n d e r l i n e a r s c a l i n g the s u r f a c e intensity ( W / m m 2) t e n d s to r e m a i n invariant and hence the total p o w e r capability goes up as ~2. This is usually fortunate since a c h i e v e m e n t of long r a n g e often y i e l d s m o s t e a s i l y to a dual attack of i n c r e a s e d p o w e r and l o w e r e d f r e q u e n c y . However, t h e r e a r e s o m e applications w h e r e g r e a t p o w e r i s not needed, and, f o r t h e s e c a s e s , r a t h e r than being guided by scaling one would seek r a d i c a l l y d i f f e r e n t d e s i g n s . One c o n s e q u e n c e of the need f o r economy of m a t e r i a l s is that r i g i d r e f l e c t o r s and rigid t r a n s d u c e r housings at audio f r e q u e n c i e s a r e c o n c e p t s that a r e s e l d o m r e a l i z a b l e p r a c t i c a l l y . Another c o n s e q u e n c e is that the p i e z o e l e c t r i c c e r a m i c o r o t h e r active m a t e r i a l m u s t be worked c l o s e r to its u l t i m a t e power l i m i t s than is usually n e c e s s a r y in u l t r a sonic t r a n s d u c e r s . M o s t a u d i o - f r e q u e n c y a r r a y s use the longitudinal v i b r a t o r type of t r a n s d u c e r e l e m e n t , s i m i l a r to the one shown in Fig 5 except made l a r g e r , lo The p r o b l e m of isolating the r e s o n a t o r f r o m its housing i n c r e a s e s with o p e r a t i n g depth, and oil filling is not a g e n e r a l l y a c c e p t a b l e solution to the depth p r o b l e m . Line a r r a y s a r e usually m a d e up of r i n g - t y p e t r a n s d u c e r s . Fig 7 shows a c e r a m i c ring v i b r a t o r that is built up out of c e r a m i c s e g m e n t s . In this type of c o n s t r u c t i o n the e l e c t r o d e s a r e on the c e r a m i c s u r f a c e s that a r e bonded in f o r m ing the joints. Hence the e l e c t r i c field is c i r c u m f e r e n t i a l , t h e r e b y being optimally coupled to the v i b r a t i o n s (k33 coupling). B e s i d e s making this field p o s s i b l e , s e g m e n t e d cons t r u c t i o n also allows the r i n g s to be built in much l a r g e r s i z e s than would be p o s s i b l e if they w e r e monolithic. Since production of c e r a m i c p i e c e s with any d i m e n s i o n much l a r g e r than 150 m m i s usually not e c o n o m i c a l , s e g m e n t e d c o n s t r u c t i o n is u s e d a g r e a t deal in l o w - f r e q u e n c y t r a n s d u c e r s . Although the epoxy c e m e n t s u s e d in the joints a r e an o r d e r of magnitude m o r e compliant than the c e r a m i c , the j o i n t s may be m a d e so thin that t h e i r effect on the r e s o n a n t f r e q u e n c y is s c a r c e l y n o t i c e a b l e . Also, p r o p e r l y made joints a r e a s s t r o n g as the c e r a m i c itself. However, the s t r e n g t h of the c e r a m i c in t e n s i o n is not a s high a s one would like (only about 2 x 107Nm - 2 in l a r g e p i e c e s ) , and hence p r e s t r e s s i n g t e c h n i q u e s such a s i l l u s t r a t e d in F i g s 5 and 7 a r e very important.

ULTRASONICS October 1970

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F i g 7 Segmented p i e z o e l e c t r i c c e r a m i c r i n g s . The r i n g a t the right has been wound with g l a s s f i b r e s under tension to p r e s t r e s s the c e r a m i c . Lead z i r c o u a t e t i t a n a t e r i n g s ; 2 5 0 m m dia; r e s o n a t e in a i r at about 4kHz.

One way to u s e r i n g s in a line a r r a y is to stack t h e m axially and t e r m i n a t e the stack with stiff end caps, with a i r o r s o m e o t h e r p r e s s u r e - r e l e a s e m a t e r i a l left inside. Such a t r a n s d u c e r h a s a depth l i m i t a t i o n , s i n c e i n c r e a s i n g s e a - p r e s s u r e c a u s e s the c i r c u m f e r e n t i a l s t r e s s in the c e r a m i c to build up to a point w h e r e the c e r a m i c p r o p e r t i e s change e x c e s s i v e l y and e v e n t u a l l y f r a c t u r e o c c u r s . F o r g r e a t depths, t h e r e f o r e , f r e e - f l o o d i n g c o n s t r u c t i o n , in which all s u r f a c e s of the r i n g s a r e exposed to the h y d r o s t a t i c p r e s s u r e and a r e allowed to r a d i a t e sound, is used. Of c o u r s e a c e r a m i c r i n g m u s t b e p r o t e c t e d f r o m s e a water; so it o p e r a t e s in an oil bath cont a i n e d in a r u b b e r e n c l o s u r e . F i g 8 shows a t r a n s d u c e r of t h i s type.

Fig 8 A p i e z o e l e c t r i c t r a n s d u c e r d e v e l o p e d by International T r a n s d u c e r Corp with ring s i m i l a r to the one shown in F i g 7 mounted in an o i l - f i l l e d e n c l o s u r e . The unit at the top of the s t r u c t u r e i s a container f o r the tunin~ and matching comp(ments. D e s i g n e d for 2kW Input o v e r the 3 - 4 k H z band.

At one t i m e it was thought t h a t f r e e - f l o o d i n g r i n g s would not be v e r y useful b e c a u s e of the c a n c e l l a t i o n that t e n d s to take place between the r a d i a t i o n f r o m the i n s i d e and outside s u r f a c e s , which a r e a c o u s t i c a l l y 180 ° out of p h a s e . But with the r i g h t p r o p o r t i o n s v e r y good r e s u l t s a r e achieved, e s p e c i a l l y if the cavity r e s o n a n c e of the e n c l o s e d w a t e r c o l u m n is exp l o i t e d . l l A r r a n g e m e n t s in which the outside s u r f a c e of the r i n g is not allowed to r a d i a t e have also b e e n t r i e d , 12 but a c h i e v i n g the r e q u i r e d a c o u s t i c s h i e l d i n g is a p r o b l e m at g r e a t depths. The t r a n s d u c e r of F i g 8 c o n t a i n s a single ring, and its r a d i a t i o n p a t t e r n is t o r o i d a l with the m a x i m u m output in d i r e c t i o n s p e r p e n d i c u l a r to the c y l i n d r i c a l s u r f a c e . A capped r i n g c a n be d e s i g n e d to have an output in the axial d i r e c t i o n that is c o m p a r a b l e to the output in the p l a n e of the ring, but t r u e o m n i d i r e c t i o n a l i t y is not a c h i e v a b l e at the r e s o n a n t frequency. Although s e g m e n t e d c e r a m i c r i n g s m a y be m a d e m u c h l a r g e r than t h o s e shown in F i g 7, the i n h e r e n t f r a g i l i t y of the c e r a m i c p r e v e n t s p u s h i n g t h i s t e c h n i q u e to e x t r e m e s . Magn e t o s t r i c t i v e m e t a l r i n g s , on the o t h e r hand, a r e s t r o n g and well adapted to c o n s t r u c t i o n in l a r g e s i z e s . F i g 9 shows r i n g s of t h i s type m a n u f a c t u r e d by Bendix, E l e c t r o d y n a m i c s Div. They a r e m a d e of c o b a l t - n l c k e l s h e e t m e t a l wound in s c r o l l f a s h i o n and c o n s o l i d a t e d with an epoxy c e m e n t . F o r o m n i d i r e c t i o n a l r a d i a t i o n in the a u d i o - f r e q u e n c y range, l a r g e s p h e r i c a l c e r a m i c s h e l l s have been built up out of t r i a n g u l a r s e g m e n t s . T h e i r cost and f r a g i l i t y have p r e v e n t e d t h e m f r o m b e c o m i n g widely used. The d i a m e t e r of r i n g t r a n s d u c e r s and s p h e r i c a l s h e l l t r a n s d u c e r s o p e r a t i n g at r e s o n a n c e is, v e r y roughly, one wavelength in water, although the r i n g s m a y be s u b s t a n t i a l l y s m a l l e r when t h e i r c a v i t y r e s o n a n c e is used. If the p o w e r 248

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Fig 9 Large m~etostrictive r i n g s . W i r e with p o l y e t h y l e n e w a t e r p r o o f i n g i s wound on the rings, and t h e s e windings c a r r y both dc b i a s c u r r e n t and a c s i g n a l .

a f f o r d e d by t h e s e l a r g e r e s o n a t o r s is not needed, the u s e r n a t u r a l l y p r e f e r s s o m e t h i n g m o r e c o m p a c t and l i g h t e r . When o m n i d i r e c t i o n a l radiation is r e q u i r e d , it can be p r o d u c e d by any s m a l l s o u r c e that is f r e e of a n t i p h a s a l radiating s u r faces.

Another type of f l e x u r a l v i b r a t o r is the e n d - s u p p o r t e d f l e x u r a l b a r . Fig 12 shows a t r a n s d u c e r c o n s i s t i n g of six f l e x u r a l b a r s a r r a n g e d in b a r r e l stave fashion. The b a r s a r e m a d e of two l a y e r s of c e r a m i c , but e a c h l a y e r in t u r n is constructed from many segments.

One a p p r o a c h to producing a s m a l l monopole is to m i n i a t u r i z e (in wavelength m e a s u r e ) a longitudinal v i b r a t o r such a s shown in Fig 5. F i g 10 shows one such design. Since o m n i d i r e e t i o n a l i t y is d e s i r e d , the longitudinal v i b r a t o r is m a d e d o u b l e - e n d e d (both m a s s e s radiate). The ratio of endm a s s a r e a to c e r a m i c c r o s s - s e c t i o n is made e x t r e m e l y l a r g e , and this p r o d u c e s a low r e s o n a n t f r e q u e n c y in r e l a t i o n to t r a n s d u c e r s i z e . Similar p r i n c i p l e s w e r e u s e d by Abbott, 14 but for l o w e r f r e q u e n c y t r a n s d u c e r s . D e s i g n s which did not utilize c u r v e d h e a d s w e r e p r o d u c e d by W e b e r of Hudson L a b o r a t o r i e s (unpublished) and by Lubell. 15

Fig 13 shows a type of t r a n s d u c e r called ' f l e x t e n s i o n a l . ' The c e n t r a l c e r a m i c stack v i b r a t e s extensionally, while the s u r rounding m e t a l shell, which f o r m s the radiating s u r f a c e , v i b r a t e s in f l e x u r e . The g e r m i n a l p r i n c i p l e s of such d e v i c e s

The m i n i a t u r i z e d longitudinal v i b r a t o r s u s e s l e n d e r c e r a m i c s t a c k s , which a r e r a t h e r e a s i l y b r o k e n . In seeking c o m p a c t l o w - f r e q u e n c y r e s o n a t o r s it s e e m s m o r e n a t u r a l to u s e f l e x u r a l m o d e s r a t h e r than longitudinal m o d e s . To excite f l e x u r a l motion p i e z o e l e c t r i c a l l y we u s e b i l a m i n a r c o n s t r u c tion. Two l a y e r s of c e r a m i c a r e c e m e n t e d t o g e t h e r and d r i v e n e l e c t r i c a l l y in such a way that one l a y e r expands when the o t h e r c o n t r a c t s . The t r a n s d u c e r shown in Fig 11 c o n t a i n s two b i l a m i n a r d i s k s that a r e mounted on a c o m m o n edge support ring and have an a i r s p a c e b e t w e e n t h e m . The d i s k s f o r m a balanced v i b r a t o r , which r a d i a t e s a s a m o n o pole. The unit is e n c a p s u l a t e d in polyurethane for w a t e r proofing. L a r g e r t r a n s d u c e r s b a s e d on the s a m e p r i n c i p l e s can handle m u c h m o r e power. 16

Fig 10 A miniatttre longitudinal vibrator d e v i s e d by W i l l i a m s and H~mlin 13 The end m a s s e s a r e cupped d i s k s which a l m o s t m e e t each other at their e d g e s but l e a v e a s m a l l gap s e a l e d by a rubber band.

Fig 12 H o n e y w e l l f l e z u r a l bar t r a n s d u c e r . 2 5 0 m m dta and the o v e r a l l length i s 600ram. T h i s lead z i r c o n a t e titanate t r a n s d u c e r r a d i a t e s 15W at i t s r e s o n a t e frequency of 145Hz.

~ ii!ii!i!~i~i~i!~i~i!i!~ii!i~i~i~Ii

F i g 11 Double f l e x a r a l d i s k t r a n s d u c e r p r o d u c e d by A M E T E K / S t r a z a . The d i a m e t e r i s 1 0 0 m m and the resonant f r e q u e n c y i s l k H z . T h i s b a r i u m t/t~n~te t r a n s d u c e r handles 4W and o p e r a t e s to depths of 150m.

Fig 13 F l e x t e n s i o n a l t r a n s d u c e r developed by North A m e r i c a n R o c k w e l l / A u t o n e t i c s . The major a x i s i s 170ram and the minor a x i s i s 80ram. End p l a t e s (not shown) a r e u s e d for waterproofing. This lead z i r c o n a t e Utanate t r a n s d u c e r has i t s m a x i m u m output at about 2500Hz.

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w e r e given by Abbott, 17 and a s e r i e s of d e s i g n s was d e v e l oped by Toulis. In addition to the oval c y l i n d e r type of Fig 13, he developed t r a n s d u c e r s in the f o r m of f i g u r e s of r e v lution, for example, a p r o l a t e s p h e r o i d a l shell d r i v e n by a c e n t r a l stack of p i e z o e l e c t r i c c e r a m i c d i s k s , i s o r an oblate s p h e r o i d a l shell d r i v e n by a single disk lying in its equat o r i a l plane. The v a r i a b l e r e l u c t a n c e and the m o v i n g - c o i l d r i v i n g m e c h a n i s m s still find o c c a s i o n a l use in l o w - f r e q u e n c y t r a n s d u c e r s . A n e w e r d e v e l o p m e n t is the h y d r o a c o u s t i c t r a n s d u c e r , 18, 19,2(] which u s e s an e l e c t r i c a l l y c o n t r o l l e d valve and hydraulic p i s t o n s to d r i v e radiating m e m b e r s into o s c i l l a t o r y motion. T h e s e t r a n s d u c e r s a r e m o s t a t t r a c t i v e at f r e q u e n c e s below a few k i l o h e r t z . They a r e not r e s t r i c t e d to the s m a l l - s o u r c e c a t e g o r y but may be m a d e with l a r g e radiating f a c e s if d e s i r e d . An i m p o r t a n t advantage is t h e i r ability to u s e hydraulic e n e r g y s t o r a g e , in low d u t y - c y c l e pulse s y s t e m s . All the s m a l l s o u r c e s d i s c u s s e d above will be c r u s h e d by s e a p r e s s u r e when m o d e r a t e depths a r e e x c e e d e d u n l e s s they a r e i n t e r n a l l y p r e s s u r i z e d . But being low m e c h a n i c a l impedance d e v i c e s they cannot t o l e r a t e a h i g h - i m p e d a n c e p r e s s u r i z i n g medium, such as u n r e l i e v e d oil, u n l e s s design c o m p r o m i s e s a r e m a d e . 21 Dipole s o u r c e s have had little use in u n d e r w a t e r sound, the notable exception being the v a r i a b l e r e l u c t a n c e ' s h a k e r box' developed by the US Naval R e s e a r c h L a b o r a t o r y and m a d e in s e v e r a l d e s i g n m o d i f i c a t i o n s by M a s s a / D C A . 22 Small s o u r c e s , including dipoles, may be u s e d in a r r a y s to f o r m d i r e c t i v e b e a m s . A p l a n a r a r r a y of s m a l l s o u r c e s n o r m a l l y would f o r m a b i d i r e c t i o n a l s e a r c h l i g h t p a t t e r n u n l e s s a r e f l e c t o r w e r e u s e d to e l i m i n a t e the back lobe. T h r e e - d i m e n s i o n a l a r r a y s p h a s e d to e l i m i n a t e the back lobe provide a n o t h e r solution to this p r o b l e m . Although a c o n c r e t e h o r n weighing 8000kg has b e e n built for u n d e r w a t e r use, 22 such heavy r e f l e c t i n g d e v i c e s a r e s e l d o m used. Instead p r e s s u r e - r e l e a s e e l e m e n t s , such a s the c o m pliant m e t a l tube, 23 a r e used for r e f l e c t o r s 24 and l e n s e s at audio f r e q u e n c i e s . Fig 14 shows a c o m p l i a n t - t u b e r e f l e c t o r d e s i g n e d to o p e r a t e at about 4kHz. It is fed by a f l e x t e n sional t r a n s d u c e r and p r o d u c e s a b e a m 18 ° wide. The o p e r a t ing depth is 1200m, but p r e s s u r e c o m p e n s a t i o n of the tubes with c o m p r e s s e d a i r is r e q u i r e d . B e a m - f o r m i n g r e f l e c t o r s a r e advantageous when the high p o w e r obtainable f r o m an e q u i v a l e n t - a p e r t u r e t r a n s d u c e r a r r a y is not r e q u i r e d . In the mobile application shown, the open c o n s t r u c t i o n is a vital

advantage b e c a u s e of the need for m i n i m i z i n g h y d r o d y n a m i c drag. In addition to active s o n a r s y s t e m s , which n o r m a l l y u s e the s a m e t r a n s d u c e r s for both t r a n s m i t t i n g and r e c e i v i n g , many applications e x i s t f o r p a s s i v e l i s t e n i n g s y s t e m s of m u l t i octave bandwidth. Since the w a t e r n o i s e at audio f r e q u e n c i e s is v e r y high r e l a t i v e to t h e r m a l n o i s e (Fig 2), v e r y low efficiency in the h y d r o p h o n e s is a c c e p t a b l e . Hence s m a l l , n o n - r e s o n a n t t r a n s d u c e r s a r e adequate for u s e in listening a r r a y s . The dominant s y s t e m n o i s e is usually that of the r e c e i v i n g a m p l i f i e r r a t h e r than the Johnson n o i s e of the hydrophone l o s s - r e s i s t a n c e . 25 C y l i n d r i c a l c e r a m i c tubes with end caps a r e the m o s t -Apular type of hydrophone. For m o d e r a t e depths they have ~_ e s s u r e - r e l e a s e d i n t e r i o r s , w h e r e a s for d e e p e r applications they a r e filled with oil. Since the tubes a r e n o n - r e s o n a n t in the operating range, they have high m e c h a n i c a l i m p e d a n c e and t h e i r p e r f o r m a n c e is only m o d e r a t e l y d e g r a d e d by the oil i m p e d a n c e . 28 F o r shallow depths, flexural disk t r a n s d u c e r s , such a s shown in Fig 11, d e s i g n e d with the r e s o n a n c e above the top of the listening band make e x c e l l e n t h y d r o phones. In the lower audio and subsonic r e g i o n s of the s p e c t r u m t h e r e is much activity in s e i s m i c profiling, 27 p r i n c i p a l l y f o r oil exploration along the continental shelf. The objective is to delineate s u b - b o t t o m s e d i m e n t a r y l a y e r s , and v e r y low f r e q u e n c i e s a r e r e q u i r e d to achieve the d e s i r e d p e n e t r a t i o n . Hydroacoustic t r a n s d u c e r s a r e u s e d to s o m e extent in the work, but the main e m p h a s i s is on e x p l o s i o n - s i m u l a t i o n d e v i c e s . 28

CURRENT PROBLEMS IN UNDERWATER SOUND TRANSDUCERS Producing t r a n s d u c e r s that maintain t h e i r w a t e r t i g h t integrity is a p r o b l e m that can n e v e r be c o n s i d e r e d to be solved once and for all. The n e c e s s a r y technology is available, but the painstaking effort r e q u i r e d to apply it s u c c e s s f u l l y is often u n d e r e s t i m a t e d by the d e s i g n e r s and the quality c o n t r o l e n g i n e e r s . In this connection it m u s t not be forgotten that i n t e n s e acoustic v i b r a t i o n s put a s t r a i n on w a t e r t i g h t s e a l s ; a t r a n s d u c e r that p a s s e s a s t a t i c p r e s s u r e t e s t may develop leaks when it is o p e r a t e d at full p o w e r u n d e r the s a m e h y d r o static p r e s s u r e . B e c a u s e the lmxury of g e n e r o u s safety f a c t o r s can s e l d o m be a f f o r d e d in l o w - f r e q u e n c y t r a n s d u c e r s , they a r e p r o n e to i n t e r n a l f a i l u r e u n l e s s g r e a t c a r e is taken to avoid s t r e s s r i s e r s , c o r o n a points, vapour p e r m e a t i o n , and m a t e r i a l s of s u b s t a n d a r d quality. An added burden in the design of naval t r a n s d u c e r s is the r e q u i r e m e n t that they s u r v i v e explosive shock. The d i s c u s s i o n of t r a n s d u c e r d e s i g n s in the e a r l i e r s e c t i o n s brought out the fact that providing ' p r e s s u r e r e l e a s e ' is a b a s i c p r o b l e m . In the s i n g l e - e n d e d l o n g i t u d i n a l - v i b r a t o r t r a n s d u c e r the p r o b l e m is one of a c o u s t i c isolation of the v i b r a t o r f r o m its housing. We can i m a g i n e the v i b r a t o r being held by a s p r i n g s u s p e n s i o n s y s t e m ; the s p r i n g s m u s t be s t r o n g enough to withstand the h y d r o s t a t i c f o r c e e x e r t e d on the radiating face; yet they m u s t be compliant enough to p r o vide vibration isolation. T h e s e r e q u i r e m e n t s tend to be c o n t r a d i c t o r y and the p r o b l e m is to achieve a c o m p r o m i s e solution. The higher the c o m p l i a n c e , the higher is the static d i s p l a c e m e n t that m u s t be a c c o m m o d a t e d and the h i g h e r the e n e r g y s t o r e d in the s p r i n g s . E n e r g y s t o r a g e of c o u r s e takes up space.

Fig 14 Paraboloidal reflector transducer s y s t e m developed by North A m e r i c a n R o e k w e l l / A u t o n e t i c s and mounted on the deep s u b m e r s i b l e Star HI. The transducer v i s i b l e on the forward boom i s a r e c e i v i n g hydrophone; the one feeding the reflector is obscured. 250

ULTRASONICSOctober 1970

Fig 15 shows s c h e m a t i c a l l y the c h a r a c t e r i s t i c s of s p r i n g s that might be used for supporting the v i b r a t o r . A conventional l i n e a r s p r i n g may be adequate, but b e t t e r r e s u l t s a r e often obtainable f r o m the nonlinear s p r i n g s s i n c e t h e i r c o m p l i a n c e is high over p a r t of t h e i r operating r a n g e . F i b r o u s m a t e r i a l s such a s p a p e r 29 a r e h a r d s p r i n g s ; t h e i r i n c r e m e n t a l c o m pliance d e c r e a s e s at high p r e s s u r e . No p r a c t i c a l m a t e r i a l s that have the opposite c h a r a c t e r i s t i c of i n c r e a s e d c o m p l i a n c e at high p r e s s u r e a r e known. To achieve this effect one must r e l y i n s t e a d on g e o m e t r y ; the B e l l e v i l l e s p r i n g 30 is such an e x a m p l e in which a d e s i r a b l e nonlinear c h a r a c t e r i s t i c is

achiqved even though it is made of a m e t a l which obeys Hooke's law."The choice of the type of s p r i n g depends to a l a r g e extent on the g e o m e t r i c a l c o n s t r a i n t s of the design. The f i b r o u s m a t e r i a l s , for example, a r e not s e l f - s u p p o r t i n g but m u s t be u s e d in the bulk c o m p r e s s i b i l i t y mode, eg, in the f o r m of a pad b e t w e e n the r e a r m a s s and the housing. Some damping is d e s i r a b l e in the s u s p e n s i o n s y s t e m , and the fibrous m a t e r i a l s usually p r o v i d e t h i s . The damping r e d u c e s the t r a n s m i s s i o n peaks which inevitably occur, at f r e q u e n c i e s outside of the main o p e r a t i n g band, a s a r e s u l t of the r e s o n ance of the v i b r a t o r with its s u s p e n s i o n s y s t e m . Instead of supporting the longitudinal v i b r a t o r on d i s c r e t e s p r i n g s , one could fill the housing with a p r e s s u r e - r e l e a s e fluid and b a l a n c e the h y d r o s t a t i c f o r c e on the radiating head by equalizing the i n t e r n a l p r e s s u r e with the a m b i e n t p r e s s u r e . Such i n t e r n a l p r e s s u r i z a t i o n is needed in the s m a l l s o u r c e s d e s c r i b e d in the p r e v i o u s s e c t i o n . The b e s t p r e s s u r e - r e l e a s e fluid is of c o u r s e a gas. When p r e s s u r e - e q u a l i z e d with the a m b i e n t s e a it b e h a v e s like a h a r d s p r i n g , but its i n c r e m e n t a l c o m p r e s s i b i l i t y r e m a i n s much h i g h e r than that of a liquid at full ocean depths. The compliant m e t a l tube r e f l e c t o r e l e m e n t s m u s t be g a s - p r e s s u r i z e d if they a r e to be u s e d at depths much g r e a t e r than 500m. Unfortunately c o m p r e s s e d gas s y s t e m s for g r e a t depths p r e s e n t f o r m i d a b l e weight and reliability problems. Liquids can hardly qualify a s p r e s s u r e - r e l e a s e fluids. Although a few liquids p o s s e s s a 3 to 1 advantage in c o m p r e s s i b i l i t y over w a t e r at a t m o s p h e r i c p r e s s u r e , they l o s e m o s t of this advantage at ocean bottom p r e s s u r e s . When t r a n s d u c e r s a r e liquid-filled, t h e r e f o r e , the s t i f f n e s s of the liquid has an i m p o r t a n t (and usually d e l e t e r i o u s ) effect on the design. A combination of oil and p r e s s u r e - r e l e a s e e l e m e n t s , such a s compliant tubes, in the t r a n s d u c e r i n t e r i o r can p r o v i d e a good c o m p r o m i s e for m o d e r a t e depths. The t r a n s d u c e r s shown in F i g s 12 and 13 u s e this approach. D e t e r m i n i n g the p o w e r limits2O, 31 of a p r o p o s e d t r a n s d u c e r is a n o t h e r p r o b l e m of b a s i c i m p o r t a n c e . If the t r a n s d u c e r has a high m e c h a n i c a l - Q (ie, lightly loaded by radiation), then its p o w e r may be l i m i t e d by m e c h a n i c a l f r a c t u r e or fatigue. A t r a n s d u c e r that is o p e r a t e d n e a r the s u r f a c e may have a cavitation limit, and a t r a n s d u c e r that is d r i v e n with a signal of high duty c y c l e (or CW) may have a t h e r m a l limit. With many t r a n s d u c e r s , operating conditions a r e such that none of t h e s e l i m i t s is in effect and we a r e left with an e l e c t r i c a l limit, ie, an e l e c t r i c - f i e l d l i m i t for p i e z o e l e c t r i c t r a n s d u c e r s and a m a g n e t i c - f i e l d l i m i t f o r m a g n e t o s t r i c t i v e t r a n s d u c e r s . The p o w e r output at r e s o n a n c e is then given by the equation k 2

Pr = ~ma°~rQM-Ue 1 -- k 2

1

w h e r e ~ma is the m e c h a n o a c o u s t i c a l efficiency, cor is the angular r e s o n a n t f r e q u e n c y , QM is the m e c h a n i c a l s t o r a g e f a c t o r , k is the effective e l e c t r o m e c h a n i c a l coupling f a c t o r , and U e is the e l e c t r i c (or magnetic) e n e r g y s t o r a b l e in the t r a n s d u c e r when it is blocked. Equation 1 is b a s e d on the u s u a l a s s u m p t i o n that the t r a n s d u c e r is r e p r e s e n t a b l e in the f r e q u e n c y r e g i o n about r e s o n a n c e by a s i n g l e - d e g r e e - o f freedom system. F o r lead z i r c o n a t e titanate c e r a m i c , for example, the s t o r e d e n e r g y Ue is 103 J m - 3 when the driving field is 0.4kV m m -1 r m s . This value of d r i v i n g field is a r b i t r a r y ; many d e s i g n e r s would p r e f e r about half this value in the i n t e r e s t of r e l i ability; a few o t h e r s have b a s e d t h e i r d e s i g n s on values twice this high. Since p o w e r v a r i e s a s the s q u a r e of the field, we a r e talking about a 12-dB r a n g e between t h e s e e x t r e m e s . To n a r r o w this debatable r a n g e we m u s t l e a r n m o r e about the n o n l i n e a r i t i e s of p i e z o e l e c t r i c c e r a m i c s at high field and about the p e r t u r b a t i o n s that h i g h - p o w e r driving induces in t h e i r n o r m a l ageing c h a r a c t e r i s t i c s . Equation 1 p r e d i c t s that nickel m a g n e t o s t r i c t i v e t r a n s d u c e r s will d e l i v e r c o n s i d e r a b l y l e s s p o w e r than lead z i r c o n a t e titauate t r a n s d u c e r s . However, the s t r e n g t h of the m a g n e t o s t r i c t i v e m e t a l s i s an i m p o r t a n t advantage which may outweigh power c o n s i d e r a t i o n s , e s p e c i a l l y f o r ring t r a n s d u c e r s such as shown in Fig 9. Another advantage of the m a g n e t o s t r i c t i v e m e t a l s is t h e i r good t h e r m a l conductivity. 32

..d"/ IZ.

//i Oisplacement-X Fig 15 P o s s i b l e spring c h a r a c t e r i s t i c s for r e s o n a t o r s u s pension s y s t e m s . Paper i s one of s e v e r a l m a t e r i a l s that a r e u s e d in pad f o r m . The B e l l e v i l l e spring i s a s p e c i a l l y shaped m e t a l spring.

Rules of thumb for p o w e r a r e in g r e a t demand by s y s t e m p l a n n e r s . E s t i m a t e s a r e s o m e t i m e s b a s e d on the a s s u m p tion 0.1W m m -2, obtainable f r o m the s u r f a c e of the t r a n s d u c e r s u s e d in a r r a y s . This figure does not depend on t r a n s d u c e r frequency. In t e r m s of t r a n s d u c e r weight, e s t i m a t e s have been made that 200 W kg -1 should be attainable at 10kHz; this n u m b e r then v a r i e s a s the f i r s t p o w e r of the design f r e q u e n c y . Naturally t h e s e r u l e s of thumb a r e highly a p p r o x i m a t e , and u n d e r favourable conditions it is p o s s i b l e to do much b e t t e r . If the t r a n s d u c e r is t h e r m a l l y limited, the f r e q u e n c y d e p e n d e n c i e s given above a r e not reliable. In c o n s i d e r i n g the m a t h e m a t i c a l p r o b l e m s a s s o c i a t e d with t r a n s d u c e r d e s i g n we b r e a k the p r o b l e m down into two p a r t s : single e l e m e n t d e s i g n and a r r a y d e s i g n . Not all t r a n s d u c e r s a r e u s e d in a r r a y s ; f o r t h o s e that a r e , this breakdown i s not c o m p l e t e l y s u c c e s s f u l , but it is a useful initial attack on the problem. In the d e s i g n of the t r a n s d u c e r e l e m e n t , the f i r s t a s s u m p t i o n that is n o r m a l l y made is that the t r a n s d u c e r is of the f i x e d v e l o c i t y - d i s t r i b u t i o n type, 33 ie, the deflection p r o f i l e of the r a d i a t i n g s u r f a c e at a single f r e q u e n c y is i n v a r i a n t with r e s p e c t to loading or driving conditions. The radiating s u r f a c e can then be t r e a t e d a s a single p o r t , and the c o m p l e t e t r a n s d u c e r is r e p r e s e n t a b l e as a t w o - p a r t t r a n s m i s s i o n n e t w o r k (assuming a single p a i r of w i r e s f o r the e l e c t r i c a l connections). The s e c o n d a s s u m p t i o n i s that the t r a n s d u c e r b e h a v e s like a l i n e a r s y s t e m . In g e n e r a l , the i n t e r i o r of the t r a n s d u c e r is analyzed as a d i s t r i b u t e d - p a r a m e t e r network. To compute the behaviour in the neighbourhood of the t r a n s d u c e r r e s o n ance, one may often a p p r o x i m a t e the d i s t r i b u t e d - p a r a m e t e r n e t w o r k by a l u m p e d - p a r a m e t e r network. The availability of h i g h - s p e e d c o m p u t e r s , h o w e v e r , has made the l a s t s t e p unnecessary; wide-frequency-range responses curves are now r e a d i l y obtainable once a sufficient i n v e s t m e n t in c o m p u t e r p r o g r a m m i n g has b e e n made. Some l o w - f r e q u e n c y t r a n s d u c e r s a r e truly l u m p e d - p a r a m e t e r s y s t e m s ; t h e i r a n a l y s i s i s well c o v e r e d in many textbooks. 9 The b e s t known d i s t r i b u t e d - p a r a m e t e r a n a l y s i s is that of the longitudinally vibrating b a r by Mason. 34 It f o r m s the b a s i s for the design of c o m p o s i t e longitudinally vibrating t r a n s d u c e r s (Fig 8). C o m p u t e r i z a t i o n of t h i s design p r o c e d u r e was initiated by the US Naval U n d e r s e a R e s e a r c h and Developm e n t C e n t r e and c a r r i e d to a high d e g r e e of s o p h i s t i c a t i o n . 4 Some t r a n s d u c e r s t r u c t u r e s have not yielded to a n a l y t i c a l m e t h o d s . A f i n i t e - e l e m e n t a p p r o a c h using c o m p u t e r s f r o m the s t a r t is then a p p r o p r i a t e ; the f l e x t e n s i o n a l t r a n s d u c e r was handled this way. 18 In a r r a y a n a l y s i s 35 we m u s t solve two a c o u s t i c p r o b l e m s . We m u s t obtain an a l g o r i t h m for calculating the f a r f i e l d p a t t e r n f r o m the s e t of t r a n s d u c e r v e l o c• i t .i e s {V~}, and we . J m u s t compute the s e l f - and m u t u a l - r a d i a t i o n I m p e d a n c e s

1

zij = viv----~ fs~ pi(ri)v~(~j)dSj, ULTRASONICS October 1970

2 251

w h e r e Pi(ri) is the sound p r e s s u r e p r o d u c e d by the ith t r a n s ducer, vj(r]) is the n o r m a l - v e l o c i t y d i s t r i b u t i o n function of the jth tran~dffcer, S] is the r a d i a t i n g a r e a of the jth t r a n s d u c e r , and V i and V i a r e the velocity a m p l i t u d e s of the two t r a n s d u c e r s . Wheh i = j this e x p r e s s i o n g i v e s the s e l f - r a d i a t i o n i m p e d a n c e . A t h i r d a c o u s t i c p r o b l e m a r i s e s when the a r r a y is at such a shallow depth that it is p r o n e to cavitate. Then it is n e c e s s a r y to map the p r e s s u r e a m p l i t u d e in the n e a r field in o r d e r to identify and m i n i m i z e p r e s s u r e hot s p o t s . 36

zVi

Vj = i="~l ' J V j = Z s e l f + i

vi Zij Vjj

3

w h e r e N is the n u m b e r of t r a n s d u c e r s in the a r r a y . U n f o r tunately, c l a s s i c a l a n a l y t i c a l methods yield a solution to equation 2 only for a few i d e a l i z e d g e o m e t r i e s . F u r t h e r p r o g r e s s is made p r i n c i p a l l y by n u m e r i c a l m e t h o d s , usually b a s e d on an i n t e g r a l f o r m u l a t i o n 37 of a c o u s t i c r a d i a t i o n , and p r o g r e s s is slow. However, a n a p p r o x i m a t e knowledge of the r a n g e of v a r i a t i o n of the r a d i a t i o n i m p e d a n c e {Zj} o v e r the a r r a y is often sufficient, and a r e a s o n a b l e e s t i m a t e b a s e d on the s o l v a b l e c a s e s can usually be obtained. Fig 16 shows a r e p r e s e n t a t i o n of a t r a n s d u c e r in an a r r a y when m o d u l a r d r i v e is used, ie, when each t r a n s d u c e r is d r i v e n by a s e p a r a t e a m p l i f i e r . If the a r r a y is c o m p o s e d of i d e n t i c a l t r a n s d u c e r s and e v e r y t r a n s d u c e r s e e s the s a m e baffle conditions (common a s s u m p t i o n s ) , then Z s e l f i s the s a m e for e v e r y t r a n s d u c e r . T h i s is the m o t i v a t i o n for showing Zseif s e p a r a t e l y in Fig 16. The r e m a i n i n g p a r t of the r a d i a t i o n i m p e d a n c e , shown in the box, is the p a r t that v a r i e s f r o m t r a n s d u c e r to t r a n s d u c e r . The t r a n s d u c e r is a s s u m e d to obey the l i n e a r i t y and fixed velocity d i s t r i b u t i o n a s s u m p tions; h e n c e it can be r e p r e s e n t e d by t w o - p o r t p a r a m e t e r s such a s the i m p e d a n c e m a t r i x or the g e n e r a l c i r c u i t p a r a m e t e r m a t r i x . F o r p u r p o s e of a n a l y s i s the a m p l i f i e r is taken to be a l i n e a r though u n i l a t e r a l device. The solution of the a r r a y n e t w o r k is a s t r a i g h t f o r w a r d a p p l i c a t i o n of c i r c u i t theory, although for a l a r g e a r r a y the n u m e r i c a l c o m p l e x i t y may tax the ability of the l a r g e s t c o m p u t e r s . We a r e dealing with an N x N a r r a y of equations, s i n c e e v e r y t r a n s d u c e r i s coupled to e v e r y o t h e r (through the Zij t e r m s in the box on the right). The v a r i a b l e p a r t of the r a d i a t i o n i m p e d a n c e , shown in the box, is the s o u r c e of difficulties in a r r a y d e s i g n s i n c e it can be d i f f e r e n t for e v e r y t r a n s d u c e r in the a r r a y . T h e t r a n s d u c e r s would work b e s t if they all had the s a m e r a d i a t i o n load, but this s i t u a t i o n n e v e r e x i s t s in p r a c t i c a l a r r a y s . D e s i g n e r s a r e v e r y m u c h i n t e r e s t e d in ways to m i n i m i z e the effects of the v a r i a b l e p a r t of the r a d i a t i o n i m p e d a n c e on the array behaviour. One of the m o s t s a t i s f a c t o r y ways to m i n i m i z e t h e s e effects is to m a k e N Vi Zseif ~ ~ . ziJ v~. •

To r e a l i z e this condition one would m a k e the d i a m e t e r of the t r a n s d u c e r r a d i a t i n g head l a r g e in t e r m s of w a v e l e n g t h s . However, for p r o p e r b e a m f o r m i n g it is usually n e c e s s a r y that the d i a m e t e r b e l e s s than a half wavelength; so the a r r a y u n i f o r m i t y a c h i e v a b l e by this a p p r o a c h is l i m i t e d . O t h e r a p p r o a c h e s to a r r a y d e s i g n depend on s e l e c t i o n of a p a r t i c u l a r t r a n s d u c e r v a r i a b l e (eg, velocity, f o r c e , o r voltage) a s b e i n g the m o s t c r i t i c a l one. Then the d e s i g n is a i m e d at m i n i m i z i n g the v a r i a t i o n s in the c h o s e n v a r i a b l e o v e r the a r r a y . F o r example, suppose that the t r a n s d u c e r s a r e v e l o c i t y - l i m i t e d (subject to f r a c t u r e o r fatigue); then it is d e s i r a b l e for e a c h t r a n s d u c e r to h a v e the s a m e v e l o c i t y magnitude. At a given f r e q u e n c y and s t e e r i n g angle it would be p o s s i b l e in p r i n c i p l e to a d j u s t the m a g n i t u d e s of the e x c i t a t i o n s {Es,J} so that the d e s i r e d u n i f o r m i t y of {V~} J was achieved. However, when the f r e q u e n c y o r s t e e r i n g a n g l e is changed, it would be n e c e s s a r y to p r o v i d e a new s e t of excitation a m p l i t u d e s {Esj}. T h i s is not a v e r y p r a c t i c a l p r o c e d u r e . Also, any chafiges in the t r a n s d u c e r s with t i m e 252

ULTRASONICS O c t o b e r 1970

Amp and tuning network

Transducer

,N

'.

E

Zu.VvI j

MZ_. = Fj They ~ Esj= 0 k

v

Active network

The net r a d i a t i o n i m p e d a n c e of the jth t r a n s d u c e r is

zj = Lt

IN

Es j

y

~r

Electromechanical Radiation impedance

Fig 16 Modular d r i v e of a t r a n s d u c e r in an a r r a y . E v e r y transducer in the array has such a circuit, identical except for the i m p e d a n c e box terminating the c h a i n on the right.

(due to heating, for example) would d e s t r o y the c a r e f u l l y achieved adjustments. C a r s o n 3s h a s p r o v i d e d a p r a c t i c a l solution to t h i s p r o b l e m , o v e r a l i m i t e d f r e q u e n c y r a n g e . The p r o c e d u r e is to make the m e c h a n i c a l i m p e d a n c e looking into the t r a n s d u c e r face, Zrhev , high so that

N Vi ZThev + Zself • ~ Z i j - -

i~i

vj

The T h e v e n i n i m p e d a n c e Zrhev is d e t e r m i n e d by the e x t e r n a l e l e c t r i c a l tuning e l e m e n t s as well a s by the i n t e r n a l m e c h a n i c a l e l e m e n t s of the t r a n s d u c e r , and the d e s i r e d a n t i r e s o n a n c e in ZThev is obtained by p r o p e r choice of the tuning network. C a r s o n c a l l s t h i s method of o p e r a t i o n velocity c o n t r o l . It m e a n s that {Vj} can b e found f r o m {Esj} d i r e c t l y without even knowing the r a d i a t i o n i m p e d a n c e s . It is not r e s t r i c t e d to the c a s e of u n i f o r m v e l o c i t y m a g n i t u d e s , although t h i s is p r o b a b l y its m o s t useful application. If the a r r a y is c a v i t a t i o n - l i m i t e d , keeping the f o r c e m a g n i tudes u n i f o r m o v e r the a r r a y would p r o b a b l y be b e t t e r than keeping the v e l o c i t y magnitude u n i f o r m . T h i s s i t u a t i o n then c a l l s for f o r c e c o n t r o l , which can be a c h i e v e d if Vi

"'--° Zrhev ~ Zself + i~] i Z~] Vj

6

T h i s condition i s a c h i e v a b l e o v e r a n a r r o w band if the tuning n e t w o r k is a r r a n g e d to p r o d u c e a r e s o n a n c e in ZThev, If the t r a n s d u c e r s a r e s u b j e c t to voltage b r e a k d o w n ( e l e c t r i c f i e l d - l i m i t e d ) , it would be d e s i r a b l e to have voltage c o n t r o l . In this case, one would u s e p a r a l l e l tuning, u s e an a m p l i f i e r with m i n i m u m output impedance, and m a k e the m a g n i t u d e s

of {Esi} uniform. In the discussion above it was assumed that acceptable patterns would be produced regardless of which of the distributions{V]}, {Fj}, o r {Ej} was m a d e u n i f o r m in magnitude. This of c o u r g e wduld hav~ to be v e r i f i e d in any given c a s e . Modular d r i v e a s shown in Fig 16 is not always used; s o m e t i m e s the t r a n s d u c e r s a r e fed f r o m a h i g h - l e v e l delay line, which in t u r n is fed by a single h i g h - p o w e r a m p l i f i e r . In this c a s e , a l l the t r a n s d u c e r s a r e coupled e l e c t r i c a l l y as well a s a c o u s t i c a l l y , and the a r r a y n e t w o r k a n a l y s i s b e c o m e s much m o r e l a b o r i o u s . The a n a l y s e s d i s c u s s e d above i n c o r p o r a t e the fixed velocity d i s t r i b u t i o n a s s u m p t i o n , s i n c e they a r e b a s e d on the u s e of equation 2. U n l e s s the velocity d i s t r i b u t i o n function vj(rj) is fixed in this equation, no unique a n s w e r i s obtained fo~ Zij. No p h y s i c a l r a d i a t o r s a t i s f i e s this a s s u m p t i o n r i g o r o u s l y ; a r e a l body, of c o u r s e , h a s infinite d e g r e e s of f r e e d o m and r e d u c i n g t h e s e to one (for the a n a l y s i s ) may not always be an acceptable engineering approximation. If we allow the r a d i a t o r (in the m a t h e m a t i c a l model) to have M d e g r e e s of f r e e d o m , then the n u m b e r of a r r a y equations is i n c r e a s e d f r o m N to M × N. The v i b r a t i o n of the r a d i a t i n g s u r f a c e can be r e p r e s e n t e d e i t h e r as a s e r i e s of M n o r m a l m o d e s or as the motion of M coupled r i g i d bodies. In the

mod~l method it is necessary to compute the self-radiation impedances 0f the modes and the mutual-radiation impedances which couple the modes. In the finite element method it is.necessary to compute the self- and mutual-radiation impedances of the rigid-body segments.

17

Abbott, F.R., US Patent 2,895,062, (14 July 1959) (Filed 22 December 1955).

18

Royster, L.H., 'Flextensional underwater acoustics transducer,' Journal of the Acoustical Society of America, Vol 45, No 3 (1969), pp 671-682.

This multi-degree-of-freedom approach to radiating surfaces, as well as many of the refinements mentioned in this section, is not needed in the design of most conventional transducer systems. But for low-frequency a r r a y s that are to be produced in quantity, the size and cost are so great that highly sophisticated design methods are often considered justified.

19

Crawford, A. E., 'High power sonar transducers,' Ultrasonics, Vol 5, (1967) pp 150-154.

20

Woollett, R.S., 'Power limitations of sonic transducers,' IEEE Transactions on Sonics and Ultrasonics, Vol SU-15,No 4 (1968),pp 218-229.

21

Johnson, F. H., and R. S. Woollett, 'A flexural ceramic disk transducer for deep water operation,' IEEE International Convention Record, Part 9 (1963), pp 60-64.

22

McGrath, T.D., 'Deep water sonar transducers,' Undersea Technology, Vol 9, No 7 (1968), pp 27-36.

23

Toulis, W. J., 'Acoustic refraction and scattering with compliant elements,' Journal of the Acoustical Society of America, Vol 29, No 9 (1957),pp 1021-1033.

24

Kronengold, M., and W. J. Toulis, 'Directional 420Hz sound source,' IEEE Transactions on Geoscience Electronics, Vol GE-6, No 4 (1968) pp 204-211.

25

Woollett, R. S., 'Hydrophone design for a receiving system in which amplifier noise is dominant,' Journal of the Acoustical Society of America, Vol 34, No 4 (1962), pp 522-523.

26

McMahon, G. W., 'Sensitivity of liquid-filled, end-capped, cylindrical ceramic hydrophones,' Journal of the Acoustical Society of America, Vol 36, No 4 (1964), pp 695-696.

27

Sargent, G.E.G., 'Application of acoustics and ultrasonics to marine geology,' Ultrasonics, Vol 6, No 1 (1968) pp 23-28.

28

Editorial 'Sources of seismic energy for marine exploration,' Ocean Industry, Vol 3, No 5 (1968), pp 36-41 (Part 1), No 6 (1968), pp 87-94 (Part 2).

29

Higgs, R. W., and L. J. Eriksson, 'Acoustic decoupling properties of onion-skin paper,' Journal of the Acoustical Society of America, Vol 46, No 1 (1969), pp 211-215.

30

Roark, R. J., 'F o r m u l as for s t r e s s and strain' (4th Ed., McGraw-Hill, New York, Toronto, and London, 1965), p. 254.

31

Berlincourt, D. A., Curran, D. R., and Jaffe, H. 'Piezoelectric and piezomagnetic materials and their function in transducers,' in 'Physical Acoustics,' Vol 1 Part A, ed. W. P. Mason Academic P r e s s , New York, and London (1964).

32

Neppiras, E.A., 'Some remarks on the maximum power handling capacity of resonant electromechanical transducers,' Acustica, Vol 19, No 1 (1967),pp 54-56.

33

Foldy, L. L., 'Theory of passive linear electroacoustic transducers with fixed velocity distribution,' Journal of the Acoustical Society of America, Vol 21, No 6 (1949), pp 595-604.

ACKNOWLEDGEMENTS The writer is grateful to the manufacturers who supplied the photographs and data used for the illustrations in this paper. He is indebted for help received to his colleagues at the Navy Underwater Sound Laboratory, particularly to David T. Porter for insights into array design and to John F. White for an introduction to the BeUeville spring approach to p r e s s u r e release.

REFERENCES 1

Thorp, W. H., 'Analytic description of the low-frequency attenuation coefficient,' Journal of the Acoustical Society of America, Vol 42,No 1 (1967),p 270.

2

Urick, R. J., ' P ri n ci p l e s of underwater sound for engine e r s ' , McGraw-Hill Book Co, New York, (1967).

3

Wenz, G. M., 'Acoustic ambient noise in the ocean: spectra and sources,' Journal of the Acoustical Society of America, Vol 34, No 12 (1962), pp 1936-1956.

4

Becken, B.A., 'Sonar,' in 'Advances in hydroscienee,' Vol 1, ed. V. T. Chow, Academic Press, New York and London (1964).

5

Kendig, P. M., 'Advanced transducer developments,' in 'Underwater acoustics,' Vol 2, ed. V. M. Albers, Plenum P r e s s , New York (1967).

6

Angus, H. C., and E. A. Neppiras, 'Nickel-based magnetostrictive alloys for electromechanical transducers,' Ultrasonics, Vol 7, No 3 (1969) pp 182-187.

7

Mellen, R. H., 'The thermal-noise limit in the detection of underwater acoustic signals,' Journal of the Acoustical Society of America, Vol 24, No 5 (1952), pp 478-480.

8

Romanenko, E.V., 'Miniature piezoelectric ultrasonic r e c e i v e r s , ' Soviet-Physics-Acoustics, Vol 3, No 4 (1957) pp 364-370.

9

Hunt, F. V., 'Electroacoustics' (Harvard University Press, Cambridge, 1964).

10

Schofield, D., ' T r a n s d u c e r s , ' in 'Underwater acoustics,' V. M. Albers, Plenum P r e s s , New York (1963).

11

McMahon, G.W., 'Performance of open f e r r o e l e c t r i c c e ra m i c cylinders in underwater transducers,' Journal of the Acoustical Society of America, Vol 36, No 3 (1964), pp 528-533.

34

Mason, W. P., 'Electromechanical transducers and wave f i l t e r s ' (2nd Ed. D. Van Nostrand, New York, Toronto, and London (1948).

12

Robey, D. H., 'On the radiation impedance of the liquidfilled squirting cylinder,' Journal of the Acoustical Society of America, Vol 27, No 4 (1955),pp 711-714.

35

13

Williams, A. L. W., and Hamlin, H.H. US Patent 3, 215, 977 (2 July 1965) (Filed 27 July 1960).

Sherman, C.H., 'Analysis of acoustic interaction in transducer a r r a y s ' , IEEE Transactions on Sonics and Ultrasonics, Vol SU-13, No 1 (1966), pp 9-15.

36

14

Abbott, F . R . , U S Patent 3,100,291 (6 August 1963) (Filed 25 October 1960)

Sherman, C.H., 'Effect of the nearfield on the cavitation limit of transducers', Journal of the Acoustical Society of America, Vol 35, No 9 (1963), pp 1409-1412.

15

Lubeil, A. H., 'Small-size, low-frequency utility source for underwater acoustic measurements,' Journal of the Acoustical Society of America, Vol 35, No 11 (1963), p 1903(A).

37

Schenck, H.A., 'Improved integral formulation for acoustic radiation problems,' Journal of the Acoustical Society of America, Vol 44, No 1 (1968) pp 41-58.

16

Woollett, R. S., 'Trends and problems in sonar transducer design,' IEEE Transactions on Ultrasonics Engineering, Vol UE-10, No 3 (1963), pp 116-124.

38 Carson, D. L., 'Diagnosis and cure of erratic velocity distributions in sonar projector a r r a y s , ' Journal of the Acoustical Society of America, Vol 34, No 9 (1962), pp 1191-1196. ULTRASONICS October 1970

253