Abstract:
An electro-mechanical transducer is disclosed, which provides a very low frequency wide band response from a bender (or benders) using piezoelectric cantilevers or center mounted free edge disc, providing additive output between the resonant frequencies achieving this response at great depths under equivalent free flooded conditions with additionally improved response with silicone rubber to reduce the acoustic cancellation associated with the dipole mode of vibration of the bender.

Description:
RELATED CASES 
     This application is a continuation-in-part of application Ser. No. 13/626,138, filed on Sep. 25, 2012. Priority for this application is hereby claimed under 35 U.S.C. §119(e) to commonly owned and co-pending U.S. Provisional Patent Application No. 61/539,018 which was filed on Sep. 26, 2011 and which are both hereby incorporated by reference herein in their entirety. 
    
    
     GOVERNMENT RIGHTS 
     The present invention was made, in part, with Government support under a Government contract. The Government may have certain rights in the invention. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates in general to transducers, and more particularly to underwater acoustic transducers. The present invention also relates to a transducer capable of radiating acoustic energy over a wide band of frequencies including very low frequencies and at deep depths. More particularly, the present invention relates to a multiply-resonant, piezoelectric-cantilever-type transducer mounted from a common stiff central rigid structure with the transducer operating in the bending mode and means for reducing dipole radiation cancellation effects. 
     2. Background Discussion 
     Low frequency underwater sound transducers require a large volume and compliant structure to obtain a low resonant frequency, such as 10 Hz, along with a high output level. This can be difficult to accomplish within a fixed volume at very low frequencies, even at shallow depths, and it becomes extremely challenging at deep depths where the hydrostatic pressure is high. That condition, coupled with a wide bandwidth, can be achieved with the present invention, which uses a fluid filled transducer of at least two cantilevers or one center mounted free edge disc with a common support structure. The disclosed “quad” cantilever resonant structure is similar to back-to-back tuning forks without stems providing one of the lowest flexural resonances for a given length and, because of the excitation of only the odd modes; there are no deep nulls between the modes of vibration providing a wide band response. Moreover, in accordance with the present invention the performance may be significantly improved by increasing the separation between opposite benders and replacing most of the enclosed fluid with silicone rubber. The silicone rubber may also be positioned and supported behind a dual cantilever bender pair or a single bender disc and provide significantly better performance than if replaced with a fluid such as water or the medium in which it is immersed. Although other materials such as cork with imbedded rubber or possibly paper may be considered, their compliant properties can be significantly compromised under pressure or as in the case of paper, be too stiff to cause an impedance miss-match between the bender and the fluid medium, typically water. 
     SUMMARY OF THE INVENTION 
     To accomplish the foregoing and other objects, features and advantages of the invention there is provided an improved electro-mechanical transduction apparatus that employs a symmetrical system that excites only odd bending modes, providing additive output between the successive resonant frequencies, yielding a very wide band response from very low frequencies to high frequencies, without nulls between the resonances. The device is comprised of piezoelectric cantilevers or a center mounted disc structure, driven with opposite phase on opposite sides, creating bending motion, and mounted and driven from a common stiff base along with silicone rubber for improved performance. 
     In accordance with the invention there is provided an electro-mechanical transduction apparatus that employs at least two electro-mechanical cantilever benders or at least a single bender disc attached to a common central stiff mounting structure with the option of silicone rubber for significant improved performance. In its most basic form, two of the cantilevers are mounted in the same plane on one side of the mounting structure with the free ends of the cantilevers on the opposite ends, and the other two cantilevers are mounted on the opposite side of the mounting structure. This quad arrangement may be used to form an array of these transducers by stacking additional quad units on the remaining surfaces of the support structure. Stiff plates can also be mounted on the remaining surfaces to reduce the out-of-phase cancellation of the interior and exterior radiation from the cantilever tines, leaving only acoustic radiation from the free open end of the interior cavity. Operation is in the free flooded mode with optional contained interior compliant fluid or compliant silicone rubber for improved low frequency performance and allowing operation at deep ocean depths. The quad structure may also be replaced with a pair of benders or a center mounted bender disc. 
     For shallow water operation where the hydrostatic pressure is not as great, the open ends can be blocked and the interior filled with a gas or air for greater output. Air backing can also be used under greater depths by filling the interior with compressed air. A compliant fluid or structure could also be used for greater depths. Greater output from a single structure can be obtained by adding four or more cantilever tines on the two remaining surfaces of the mounting structure with the interior filled with gas, fluid or compliant mechanical structure such as silicone rubber. 
     Although the invention described serves as a means for obtaining a significant very low frequency wide band underwater acoustic response, it could also be used in air as a source of sound. The structure could also serve as a receiver of sound or vibration, such as a microphone, hydrophone or accelerometer. 
     In accordance with one embodiment of the present invention there is provided an electro-mechanical transduction apparatus that comprises: symmetrically mounted piezoelectric driven cantilever tines with the greatest motion at its ends, along with means to reduce acoustic dipole cancellation, achieving very low frequency acoustic response because of the cantilever resonance operation and achieving wideband performance because of odd mode excitation yielding additive output between modes. The reduced dipole cancellation is achieved by altering the acoustic impedance behind the benders. 
     In accordance with other aspects of the present invention there is provided the means for stacking these bender elements to form an array of elements. There is also means provided for operation with a free flooding or contained fluid within the interior cavity of the cantilever structure and means for increasing the interior compliance. In addition to this there is also provided a means for replacing the piezoelectric tines in one plane with passive non-piezoelectric tines, such as steel or aluminum, yielding a response similar to the all piezoelectric response. Silicone rubber may be used to improve the output performance response by increasing the interior compliance, and also by extending the low frequency performance though an additional lower frequency resonance. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Numerous other objects, features and advantages of the invention should now become apparent upon a reading of the following detailed description taken in conjunction with the accompanying drawings, in which: 
         FIG. 1  schematically illustrates the quad cantilever transducer with four piezoelectric tines driven into the bending mode and mounted on a common base mounting structure. 
         FIG. 2  schematically illustrates the electrical connections for piezoelectric 31 mode tri-laminar operation with two plates of piezoelectric material mounted on a central substrate wired for bending mode operation. 
         FIG. 3   a  schematically illustrates the motion of quad structure in a symmetric mode of vibration. 
         FIG. 3   b  schematically illustrates the motion of quad structure in an anti-symmetric mode of vibration. 
         FIG. 4  illustrates the cantilever motion of the first three modes of vibration along with the initial case of no motion. 
         FIG. 5  illustrates a single cantilever of the quad structure with an end mass along with two compression rods and wired for piezoelectric operation in the 33 mode. 
         FIG. 6  illustrates a single piezoelectric element showing a margin separating the electrodes as well as two holes for two compression tie rods. 
         FIG. 7  illustrates an array of quad units along with stiff end plates. 
         FIG. 8   a  shows the response of an array of quad units with stiff end plates operating in the symmetric,  19 , and anti-symmetric mode,  20 . 
         FIG. 8   b  shows the response of an array of quad units with stiff end plates operating in the symmetric mode,  19 , spliced with the anti-symmetric mode,  20 , response. 
         FIG. 8   c  shows the response of an array of quad units with stiff end plates operating with the back piezoelectric tine section replaced with a metal parasitic tine section. 
         FIG. 9  schematically illustrates a center supported dual bender transducer composed of two tri-laminar piezoelectric drive circular plates or discs. 
         FIG. 10  schematically illustrates a center supported dual quad bender transducer composed of eight tri-laminar piezoelectric drive bender bars. 
         FIG. 10   a  schematically illustrates a center supported transducer of triangular form. 
         FIG. 11  schematically illustrates a dual bender array mounted on a stiff and massive central structure along with silicone rubber mounted on a backing plate. 
         FIG. 12  shows the in-water sound pressure level response (SPL) of the rectangular transducer array of  FIG. 11  with and without silicone rubber backing 
         FIG. 13  schematically illustrates a center supported axi-symmetric bender transducer composed of a tri-laminar piezoelectric drive circular plate with silicone rubber mounted on a circular backing plate. 
     
    
    
     DETAILED DESCRIPTION 
     In accordance with the present invention, there is now described a number of different embodiments for practicing the present invention. In the main aspect of the invention there is provided piezoelectric cantilevers mounted on a central support providing very low frequency and wide band response even at great ocean depths. The central rigid mount is important to this cantilever invention as it provides the rigid boundary conditions for the cantilever tines and because of the design symmetry, no additional masses or structures are needed for the cantilever central boundary condition on any of the tines in this quad configuration. (Additional mass is desired in the dual tine structure arrangement without the opposing dual tines.) 
     A simplified picture of the quad cantilever acoustic transducer is illustrated in the four tine,  1 , quad arrangement of  FIG. 1 . The similarity to back-to-back tuning forks, without stems, can be seen. When operated in the water there would be top and bottom plates attached to the rigid mount,  2 , and mechanically isolated from the cantilever tines with water or other more compliant fluid or structure in the interior section. This free flooding would require a rubber boot and/or potting to electrically isolate the piezoelectric benders,  1 , from the exterior water and interior water, which allows for pressure equalization and operation at great ocean depths. If the interior is to be filled with another fluid, a rubber enclosing bag or boot would be used to maintain the fluid within the interior. A major portion of the interior fluid could be replaced by silicone rubber for improved performance, and here, no endplates would be necessary. Transducers could be stacked on top of each other and used together as an array to attain a greater source level. 
       FIG. 2  schematically illustrates the wiring arrangement for the piezoelectric plates or bars,  1 , driven by voltages,  5 , and,  6 , for operation in the piezoelectric 31 mode. Because of the polarization direction,  10 , and the wired polarity shown as,  5 , and,  6 , the top and bottom piezoelectric plates,  4 , of  FIG. 2  are driven out of phase causing bending motion of the cantilever tine,  1 , mounted on structural support base,  2 . In this particular tri-laminar arrangement a central inactive substrate,  3 , is used to obtain a higher electromechanical coupling coefficient. 
       FIG. 3   a  illustrates the motion of the cantilevers at the fundamental symmetric mode of vibration of a quad section. Here the two bottom tines,  7 , are wired in the same way of the two top tines,  7 , to create this symmetric vibration shown where the top two tines move in a direction opposite the bottom two tines.  FIG. 3   b  illustrates the motion of the cantilevers at the fundamental anti-symmetric mode of vibration of a quad section. Here the two bottom tines,  7 , are wired oppositely in phase from the top two tines creating all tine motions in the same direction with the center mount moving,  2 , in the opposite direction of the four tines. 
     The cantilever is an ideal component for very low frequency wide band performance. The fundamental resonance, f r , of a cantilever bender bar of length L and thickness t may be written as f r =0.1615ct/L 2  where c is the bar sound speed in the material. The cantilever mode design has the advantage of achieving a low fundamental resonance frequency from a compact size. It has not only a size advantage, but a wideband response advantage with additive motion between the overtones. The odd quarter wavelength multiples of the overtones are not harmonically related and the first few are at 6.27f r  and 17.55f r . The cantilever is excited by reversing the phase or direction of polarization of the electric field on opposite sides of the piezoelectric cantilever bender tines. The center mounted free edge piezoelectric planar mode bender disc yields a similar response but with a larger diameter. 
     A finite element symmetry model of one tine,  1 , of the cantilever quad design, with length approximately 30 inches, is shown in  FIG. 4  mounted on the central rigid support,  2 , with symmetry planes  8  and  9 . The motion of the first three modes of cantilever vibration at 15, 125 and 395 Hz are illustrated in this figure. Although cantilever benders provide some of the lowest resonances for a given length, they are susceptible to excessive bending stress under deep operation and in these cases the design can benefit from pressure equalization. 
       FIG. 5  illustrates schematically a 33 mode design which has approximately twice the coupling coefficient of the 31 mode design of  FIG. 2 . Here, for simplicity,  FIG. 5  shows only four 33 mode piezoelectric plates,  13 , with direction of polarization indicated by the arrows,  10 . The top and bottom part of the plates,  13 , are connected out of phase to excite the bending mode of this single cantilever tine of a quad unit as illustrated in  FIG. 1 . Also illustrated is the mass,  11 , which replaces part of the piezoelectric structure of the cantilever. Use of steel, as item,  11 , allows a reduction in cost, approximately the same fundamental resonance frequency and yet an improved coupling coefficient. This is possible since there is little bending at this free end of the cantilever, and a piezoelectric section here would only add electrical capacity but little bending motion. Two high strength tie rods,  12 , are also provided to supply the needed compression on the piezoelectric material under high drive. Terminals,  5 , and,  6 , illustrate reversed phase operation between the upper and lower electrodes. 
     A larger number of thinner piezoelectric pieces,  13 , of  FIG. 5  would be used in actual practice allowing a lower voltage. One such piezoelectric piece is illustrated in  FIG. 6  with electrode surfaces,  14 , inactive substrate,  15 , and end pieces,  16 , with holes to accept the tie rods of  FIG. 5 . An alternative arrangement would be to extend electrode polarized piezoelectric material to the end of the end pieces or, eliminate the end pieces,  16 , as illustrated in  FIG. 5 . In practice, the tines of the quad elements could be made in modular form, possibly 10 modules, each containing 14 PZT piezoelectric elements with bar thickness of possibly 0.20 inches. 
       FIG. 6  schematically illustrates a possible six inch height of each quad element of this sample design, which contains 4.5 inches of piezoelectric PZT-8, active piezoelectric material, sandwiched between two 0.75″ plates of G-10 (or possibly PVC or a cast composition). Each of these plastic plates has holes large enough for high strength steel compression tie rods. These two tie rods provide the necessary compressive bias on the PZT piezoelectric material. A cross section of this arrangement is illustrated in  FIG. 6  showing the PZT with the split electrodes, allowing oppositely phased voltages or reversed polarization for obtaining operation in the bending mode. This design is referred to as a 33 mode of operation as the electric field and useful displacements are in the same direction and parallel to the direction of polarization of the piezoelectric ceramic. This direction is perpendicular to the electrode surfaces and through the thickness of the bar. Alternatively, the two end pieces may also be piezoelectric with electrodes and margin of 0.40 inches and two holes for the tie rods, increasing the fully active size to, in this case, 6 inches. 
     A specific array of quad elements is illustrated in  FIG. 7  and shows, approximately, an overall length of 60″, thickness of 24″ and 48″ height for this particular transducer example.  FIG. 7  also shows the central rigid mounting structure,  2 , along with a central support,  21 , which together with,  2 , support the end plates,  17 , on the top and bottom of the array. A significantly improved performance can be obtained by increasing the thickness of the full transducer, extending it from 24″ to 48″, and by filling most of the interior space with silicone rubber. 
     The finite element calculated sound pressure level (SPL) response for the array of  FIG. 7  with piezoelectric PZT pieces of  FIG. 6  is shown in  FIGS. 8   a ,  8   b  and  8   c  for a silicon oil partially filled condition for improved very low frequency response. The first three flexural cantilever resonances and additive wide band response are seen in  FIG. 8   a  which shows the case for symmetric drive,  19 , and anti-symmetric drive, 20. The greater reduction in the vicinity of 50 Hz of the symmetric drive,  19 , condition can be improved by splicing in the response of the symmetric drive,  20 , as illustrated in  8   b . Direct synthesis of the motions driven at the same voltage amplitude illustrated in  FIGS. 3   a  and  3   b  provide a condition where the bottom two tines,  7 , cancel each other as if they were not driven at all. This condition can also be achieved by simply not driving the bottom two tines and replacing them with a passive material such as aluminum or steel, creating a passive parasitic radiating resonator. The response for this case, where only the tines,  1 , are piezoelectric driven and the bottom tines,  7 , are steel is illustrated in  FIG. 8   c.    
     Although the focus of this teaching has been on cantilever bender bars, the same principles apply to a pair of flexural disc transducers with a center mount between the two, yielding a fundamental resonance frequency that is normally higher than the quad cantilever construction. This alternative disc configuration is schematically illustrated in  FIG. 9  showing a center post,  18 , tri-laminar planar-mode piezoelectric discs,  4 , and substrates,  3 . An additional alternative eight tine arrangement, instead of the four tine quad structure of  FIG. 1 , is illustrated in  FIG. 10 . This eight tine structure allows greater output from the piezoelectric tines,  1  and  7 , with substrates,  3 , and the square supporting stiff structure,  2 , preferably steel. A structure composed of three tine pairs,  1 ,  7 , of piezoelectric tines may be used with an equilateral triangular supporting structure instead of the square,  2 , shown in  FIG. 10 . In this regard refer to  FIG. 10   a  for an illustration of the triangular version. 
     The eight staved piezoelectric bender array shown in  FIG. 11  has been constructed to utilize silicone rubber,  22 , mounted on an aluminum back plate,  23 , with the cantilever bender array  1  mounted on a steel center mass,  24 . In the embodiment illustrated there are two separate silicon rubber blocks  22  one on either side of the center mass  24 . The benders  1  are mounted through a steel stem,  25 , which is mounted on the massive steel center mass  24  allowing each side (to the left and right in  FIG. 11 ) of the bender to operate as cantilevers. The particular silicone rubber used in this illustration is designated as RTV 615 and has a very low Young&#39;s modulus of 1.5 MPa, Poisson&#39;s ratio of 0.48 and bulk modulus of 12.5 MPa which is almost 200 times less than the bulk modulus of water, which is approximately 2,200 MPa. (An alternative, but more expensive, silicone rubber is RTV 566 with a Young&#39;s modulus of 4.2 MPa, Poisson&#39;s ratio of 0.45 and bulk modulus of 14.0 MPa.) The term RTV stands for “room temperature vulcanized.” This free flooded construction allows nearly a 20% reduction in size and yet yields an improved response shown in  FIG. 12  as curve  25 . This sound pressure level, SPL, response is seen to yield significantly more output when compared to the same transducer but without silicone rubber, represented as curve  26  in  FIG. 12 . 
     Although not shown, the silicone rubber backed response,  25 , yields a nearly omni-directional beam pattern, while response curve  26  without the silicone rubber yields a nearly dipole figure eight type beam pattern with lower radiation efficiency (Refer to  FIG. 12 ). The silicone rubber on the back side causes a miss-match with the water impedance on the front side of the array, significantly reducing the out-of-phase back radiation now allowing nearly omni-directional single-sided-radiation. This is accomplished with a more efficient higher-sound-pressure level compared to what would be obtained from the lower level dipole radiation without the silicone rubber. The higher radiation load of the nearly omni-directional radiator can be seen through the more damped resonance of curve  25  in the vicinity of 100 and 20 Hz. In addition to this, the low frequency response is extended by nearly an octave as a result of the resonance at 10 Hz. This resonance,  27 , approximates the performance of a low frequency Helmholtz type radiator through the dynamic mass of the water column behind the benders (along with the port radiation mass) and high compliance of the silicone rubber. 
     An axi-symmetric version of the rectangular transducer array of  FIG. 11  is shown in  FIG. 13 . As in the case of  FIG. 9 , it is a tri-laminar piezoelectric bender and is composed of piezoelectric discs,  4 , operating in the planar mode along with an inert substrate,  3 . As in  FIG. 11 , the steel stem mount  25  is disposed between the bender  3 ,  4  and the steel counter mass,  24 . The aluminum backing plate  23  is mounted (secured) to the steel center mass,  24 , and the annular silicone rubber  22  is mounted (secured) to the aluminum backing plate,  23 . This transducer operates the same as the rectangular transducer of  FIG. 11  but when scaled to a smaller size may be used as a simpler piston transducer which could be implemented as an array of these transducers. A one 10th scaled size axi-symmetric piston transducer response would be similar to curve  25  of  FIG. 12  but with a frequency scale of 0 to 2,000 Hz and a reduced sound pressure level (SPL). Here the piston diameter would be approximately 5.4″ and the depth would be only 2 inches making this a low-frequency, very low-profile transducer that could operate at significant depth. Greater source level and directionality would be obtained from an array of these transducers. 
     The above principles of this invention may be applied to transducers which transmit or receive acoustic waves or in a fluid or gas. The principles can also be applied to accelerometers. Moreover, the electromechanical material may be single crystal material, piezoelectric ceramic, electrostrictive, magnetostrictive or electromagnetic. Although steel, aluminum and silicone rubber RTV 615 were used in the illustrations other appropriate specific materials may be used. The piezoelectric transducer has been discussed as a trilaminar design with an inert section sandwiched between two piezoelectric sections. An alternative less expensive, but less powerful, arrangement would use a bilaminar structure with one inert layer and one active layer of piezoelectric material. 
     LIST OF REFERENCE NUMBERS 
     
         
         
           
               1 . Top piezoelectric tines 
               2 . Central rigid mount 
               3 . Inactive substrate 
               4 . Piezoelectric element 
               5 . Electrodes 
               6 . Electrodes 
               7 . Bottom piezoelectric tines 
               8 . Symmetry plane 
               9 . Symmetry plane 
               10 . Polarization arrow 
               11 . Tine end mass 
               12 . Tie rod 
               13 . Piezoelectric section 
               14 . Electrode surface 
               15 . Margin between electrodes 
               16 . End piece 
               17 . End plate 
               18 . Center support rod 
               19 . Symmetric response 
               20 . Anti-symmetric response 
               21 . End plate support beam 
               22 . Silicone rubber 
               23 . Back plate 
               24 . Center mass 
               25 . Stem 
           
         
       
    
     Having now described a limited number of embodiments of the present invention, it should now become apparent to those skilled in the art that numerous other embodiments and modifications thereof are contemplated as falling within the scope of the present invention, as defined in the appended claims.