EP0524371B1

EP0524371B1 - Sonar Transducer

Info

Publication number: EP0524371B1
Application number: EP19920104886
Authority: EP
Inventors: James W. Fitzgerald
Original assignee: KILDARE CORP
Current assignee: KILDARE Corp
Priority date: 1991-07-25
Filing date: 1992-03-20
Publication date: 1994-09-21
Anticipated expiration: 2012-03-20
Also published as: DK0524371T3; EP0524371A1; DE69200439D1; DE69200439T2

Description

The invention relates to underwater electroacoustic transducers, and more particularly to improvements in flexural-bar type acoustic sources for use in sonar systems. The present invention is concerned with improvements in the design of a modified "free-free" flexure bar transducer element, a vibratile element that thereafter sometimes is called "FLEXBAR" to distinguish it from the common "bender-bar" sonar projector element.

BACKGROUND OF THE INVENTION

Past efforts were concentrated to a very large extent on the so-called "bender-bar" transducer, which is a flexural-bar with "hinged-hinged" end conditions. In spite of those efforts, a number of inherent, generic problems remain. The bender-bar mountings, for example, inevitably result in loss of power due to structure-borne vibration and can create a severe ship or submarine habitability problem for hull-mounted transducer arrays. In addition, for hull-mounted, deployable, and towable sonar projector arrays, the bender-bar coupling through its mounting results in complex, spurious modal response that aggravates the array mutual impedance problems, severely limits the acoustic power output, and often results in unwanted back radiation.
The theoretical end conditions for an ideal hinged-hinged flexure bar (the bender-bar) are: (1) the end deflections must be zero (y = 0 for x = 0 and $x = L$
), and (2) the end bending moments must be zero ( $d²y/dx² = 0$
for x = 0 and $x = L$
). The extensive prior art has evolved three principal mounting designs for bender-bars: viz: (1) the pin-hinge; (2) the flange-hinge; and (3) the leaf-hinge. To some degree all three design approaches can be made to yield end bending moments that are small, but none of these can achieve the other requirement of end deflections being small, without adding excessive mass to the mounts. Attempts have also been made to cancel the reaction of the bender-bar on its mounting by utilizing a second bender-bar vibrating in opposite (180°) phase. This is an expensive solution, since it doubles the number of bender-bars, and of course, doubles the weight. Furthermore, it is of limited value since it is virtually impossible to match bender-bars so as to have equal amplitude and opposite phase (180°) over the required frequency band pass. This crowded prior art is set forth in some detail in a book "The Flexural Bar Transducer" written by R. S. Wollett and published by the Naval Underwater System Center, New London, CT, in 1986.
US-A 3 704 385 describes a piezoelectric transducer assembly comprising a flat disk of piezoelectric material held by bosses formed on a pair of mounting chips located at both sides of said disk. The bosses contact the element along its node line so that it may vibrate in an unrestrained manner. The patent describes the disadvantage that as the portion of the disk on one side of the node line vibrates in one direction, the portion of the disk on the other side of the node line always vibrates in an opposite direction so that the compression and rarefaction waves created on opposite sides of the node line tend to destructively interfere with each other and essentially cancel out the acoustical output. In order to solve these problems acoustical delay means are provided in the form of air vents or acoustical ports in the path of the rarefaction waves which phase delay means time-delay the compression wave by one-half wave length before this wave combines with the compression wave. This phase compensation requires additional air vents or acoustical restrictions and operates only at one particular frequency where the phase delay is just half of the wave length of the generated ultrasonic frequency.

SUMMARY OF THE INVENTION

The conventional wisdom of the sonar community has been that, "The free-free bar is free of external applied forces or reaction forces ... such a bar has no useful applications as an underwater transducer". (R. S. Woollett, The Flexural Bar Transducer, 1986, p. 203). This viewpoint presumeably has its origins in the fact that, unmodified, the free-free flexure bar radiates as an acoustic dipole with the concomitant poor radiation loading. The present invention relates to a method and means for modifying the free-free bar so that it radiates as a monopole, with greatly improved radiation loading. At the same time, the modified free-free bar retains the unique properties of being (a) nodally mounted and (b) dynamically balanced. As a direct result of these properties, the modified free-free bar has substantially zero mechanical reaction on its mounts, and exhibits essentially no structure-borne vibration. These characteristics, together with high efficiency, relatively low cost and other related properties, make this transducer element demonstrably superior to the bender-bar in virtually all sonar projector applications. To distinguish this innovative modified free-free flexure bar from the conventional hinged-hinged "bender-bar", the name "FLEXBAR" will be used throughout the remaining portions of this patent specification.

OBJECTS OF THE INVENTION

It is a principal object of the invention to provide a flexure bar sonar projector element that overcomes the inherent, generic problems of the bender-bar element; viz, problems associated with mechanical reaction on its mountings. This object is achieved by the invention as characterized in the independent claims. This invention prevents acoustic radiation from said outer portions which would be out of phase with said acoustic radiation from said central portion; and thus allowing the said underwater acoustic transducer to radiate acoustic energy into the water essentially as a monopol, rather than a dipole.
Further objects of the invention are to provide a flexure bar sonar projector element that:

has true nodal mounts ("keep your nodes clean"),
has a simple, fundamental free-free bar flexure resonant mode ("keep your modes clean"),
is dynamically balanced (virtually no reactive forces on its mountings),
has a high electromechanical coupling coefficient ( 0.3 to 0.6)
has a high electroacoustic efficiency ( 70%),
can be effectively mechanically biased (for high-power applications),
is mechanically tunable (over ∼1 octave),
is suitable for almost any acoustic array configuration plane, cylindrical, spherical, conformal, etc.),
is suitable for low-frequency arrays (over a range, 20 Hz to 2000 Hz),
is suitable for high-power array, (e.g., 0.5 mega watts acoustic output),
is suitable for broad-band arrays (∼1 octave),
can be utilized in surface ship or submarine sonar projector arrays (either sonar dome arrays or conformal arrays),
can be designed for use as an acoustic source for towed sonars or deployable sonars (e.g., active sonobuoys),
is capable of high acoustic power-to-weight ratios (typically 20 to 30 watts/pound, in water),
exhibits unilateral acoustic radiation (one face only) with a high front-to-back radiation ratio (∼60 dB),
has excellent heat dissipation (a direct thermal path to the ocean), and
is both easy to fabricate and easy to maintain quality control (individual elements can be readily mechanically tuned to within ∼1 Hertz).

Preferred details and embodiments of the invention are described in the dependent claims.
Other objects and advantages of the invention will become apparent by perusal of the following detailed description and the attendant figures and claims.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention is illustrated by the accompanying drawings of which:

Fig. 1: is a schematic sketch of a free-free bar vibrating in flexure at its lowest mode;
Fig. 2: is a schematic sketch of a free-free bar nodally mounted in a water-tight housing and radiating underwater as an acoustic "dipole";
Fig. 3: is a schematic sketch of a modified free-free bar vibrating in its lowest mode;
Fig. 4: is a schematic sketch of a modified free-free bar nodally mounted in a water-tight housing and radiating underwater as an acoustic "monopole";
Fig. 5: is an isometric sketch showing a preferred embodiment of a piezoceramic FLEXBAR;
Fig. 6-A: is a top view of the "wedge" method of applying a precompression mechanical bias to the piezoelectric stacks of the FLEXBAR;
Fig. 6-B: is a side-view section of the "wedge" method shown in Fig. 6-A;
Fig. 7: is a sketch showing the "taper-pin" method of applying a precompression mechanical bias to the piezoceramic stacks of the FLEXBAR;
Fig. 8: is a sketch showing the "taper-threaded plug" method of applying a precompression mechanical bias to the piezoceramic stacks of the FLEXBAR;
Fig. 9-A: is a top-view of a FLEXBAR designed for a resonant frequency of ∼1 KHz;
Fig. 9-B: is a side-view of the FLEXBAR of Fig. 9-A;
Fig. 9-C: is an end-view of the FLEXBAR of Fig. 9-A;
Fig. 10: is a curve showing the relative displacement of the center of the FLEXBAR of Fig. 9-B measured in air, as a function of frequency;
Fig. 11: is a curve showing the relative displacement along the FLEXBAR of the FLEXBAR of Fig. 9-B, measured in air, as a function of distance along the bar;
Fig. 12: is a curve showing the total impedance of the FLEXBAR of Fig. 9-B measured in air, as a function of frequency;
Fig. 13: is a curve showing the resonant frequency and the location of the nodes for the FLEXBAR of Fig. 9-B as a function of total added mass;
Fig. 14: is a curve showing the electromechanical coupling coefficients of the FLEXBAR design of Fig. 9-B as a function of total added mass for both k₃₃ and k₃₁ construction;
Fig. 15: is an exploded sketch showing the principal components of a sonar transducer module comprised of a plurality of FLEXBARs and termed a "FLEXDUCER" module;
Fig. 16-A: is a top view of a FLEXDUCER module comprised of 5 FLEXBARS of the design of 9-B;
Fig. 16-B: is an end view of the FLEXDUCER module of Fig. 16-A;
Fig. 16-C: is a side view of the FLEXDUCER module of Fig. 16-A;
Fig. 17-A: is a top-view sectional sketch showing design details of a FLEXBAR mounting;
Fig. 17-B: is a side-view sectional sketch showing design details of a FLEXBAR mounting;
Fig. 17-C: is an end-view sketch showing design details of FLEXBAR mountings;
Fig. 18: is an equivalent circuit representation of the FLEXDUCER module of Fig. 16-A;
Fig. 19: are curves showing both the measured and calculated transmitting response of the FLEXDUCER module of Fig. 16-A;
Fig. 20: shows the computed maximum acoustic power output and the mechanical Qm of a rectangular sonar array, comprised of a plurality of FLEXDUCER modules of Fig. 16-A as a function of the number of modules in the array;
Fig. 21: compares the measured housing vibration transmissibilities for a transducer module comprised of FLEXBARs and a transducer module comprised of the equivalent bender-bars;
Fig. 22: shows the piezoceramic plate means (k₃₁) for driving a FLEXBAR;
Fig. 23: shows the piezoceramic stack means (k₃₃) for driving a FLEXBAR;
Fig. 24: shows the piezoceramic stripe-plate means (k_sp) for driving a FLEXBAR;
Fig. 25-A: shows the drilled-hole means for mechanically tuning a FLEXBAR;
Fig. 25-B: shows the filled-hole means for mechanically tuning a FLEXBAR;
Fig. 25-C: shows the added-plate means for mechanically tuning a FLEXBAR;
Fig. 26-A & Fig. 26-B: show the slotted-plate means for mechanically tuning a FLEXBAR;
Fig. 26-C: shows the tuning-slug means for mechanically tuning a FLEXBAR;
Fig. 27-A & Fig. 27-B: show the fixed-pin means for nodal mounting of a FLEXBAR;
Fig. 27-C: shows the fixed-tab means for nodal mounting of a FLEXBAR; and
Fig. 28: shows the auto-nodal means for nodal mounting of a FLEXBAR.

PRINCIPLE OF THE FLEXBAR

The basic principle of the invention, the FLEXBAR sonar projector element, can be readily understood by referring to Fig. 1 through Fig. 4. Fig. 1 depicts an ideal elastic uniform free-free bar 1 excited by some means so as to vibrate freely in its lowest, fundamental flexure mode. Under this condition two nodes 2 develop, which represent points (or lines) of no vibration. The section of the bar between the nodal points vibrates in opposite phase to the outer sections; i.e. when the center section is flexing upward, the outer sections are flexing downward, and vice versa. Since no external forces are acting on the bar, the total momentum (both translational and rotational) must be zero; and this leads to the requirement that the total momentum of the center section must be equal (and of opposite phase) to the sum of the total momentum of end sections.
This requirement is sufficient to determine the location of the nodal points, as shown in Fig. 1, and thus, the nodal spacing is $ℓ = 0.552 x L$
, where L is the overall length of the bar.
One of the interesting properties of the free-free bar is that it can be hung from its nodal points 2 by threads 3 from overhead supports 4; then, when the bar is excited in high amplitude vibrations at its fundamental frequency, the threads experience no vibratory reaction forces, and are subjected only to the static force corresponding to the weight of the bar.
Fig. 2 shows a schematic representation of a free-free bar as an underwater acoustic source. The free-free bar 1 is mounted on its nodal points 2 by means of suitable mounting brackets 5 in an appropriate housing 6. An acoustically transparent rubber window 7 is bonded to the radiating surface of the bar and to the housing so as to form a water-tight seal, while at the same time allowing the bar to vibrate relatively freely. Air which may be at the same pressure as the water, depending on the depth, fills the interior of the housing, resulting in acoustic radiation into the water only.
Under these conditions, the free-free bar transducer radiates as a dipole, since the center section is vibrating 180° out of phase with the outer sections. As the center section of the bar moves up, it increases the water pressure as indicated by the symbol ⊕; while at the same time the outer sections move down, decreasing the adjacent water pressure, as indicated by the symbol ⊖. The reverse takes place on the succeeding portion of the vibration, when the center section is moving down and the outer sections are moving up. Thus much of the kinetic energy of the vibrating bar is wasted by hydrodynamically sloshing water back and forth between the adjacent zones. Such behavior interferes with the primary compressional acoustic waves and results in the poor acoustic radiation loading characteristic of a dipole source.
Consider now Fig. 3, where the outer sections 8A and 8B of the free-free bar 8 of length L are "bent" down at the nodal points 2 at right angles to the center section. If such a modified free-free bar is set into vibratory motion, it will have substantially the same resonant frequency and substantially the same location of nodal points as the original free-free bar. This results from the fact that the total inertia about the nodes of the "bent" ends sections are the same as the original straight end sections. In effect, the free-free bar sees "phantom" straight end sections. The modified free-free bar can also vibrate freely when suspended by threads.
The free-free bar can be further modified by shortening the "bent" end section and increasing their cross-section and mass so as to maintain the same total inertia about the nodal points. This further modified free-free bar will still vibrate at the same fundamental resonant frequency as the original free-free bar, and with the same locations of nodal points. Such a flexure bar is designated a "FLEXBAR".
Fig. 4 is a schematic representation of a FLEXBAR, as an underwater acoustic source. The FLEXBAR 9 is mounted on its nodal points 2 by suitable mounting brackets 5 in an appropriate housing 10. A combination cover-window 11 is bonded to the radiating surface of the FLEXBAR so as to form a water-tight seal. The end-section masses have clearance from the cover plate in those areas 12 beyond the nodal points so that the FLEXBAR can vibrate freely. As before, the interior of the housing is air-filled so that the FLEXBAR radiates only into the water.
In this configuration, the center section between nodes is the only section of the FLEXBAR that is acoustically coupled to the water. The out-of-phase modified end sections vibrate entirely in the air-filled housing and are effectively decoupled from the water. This results in the desired monopole radiation, while at the same time the FLEXBAR is nodally mounted and essentially dynamically balanced. Thus, the FLEXBAR exhibits excellent radiaton characteristics and virtually no reaction forces on the mountings and mechanical coupling to the housing.
This improvement of the free-free flexure bar has unexpected, profound, and far-reaching consequences on the performance of low-frequency, high-power, broad-band sonar transducer arrays.
As Fig. 4 shows, when the center section flexes upward the outer sections 8A and 8B flex inward therewith compressing the air under the center section. This assists the upward flexing of the center section. When the center section flexes downward and the outer sections flex outward, the same enhancing effect appears with opposite phase.
The preferred embodiment of the invention is an electroacoustic underwater transducer element that is basically a piezoceramic "free-free" flexure bar, but modified so as to radiate as a "monopole" rather than as a "dipole", and retaining the unique properties of being nodally mounted and dynamically balanced. One of the important consequences is the fact that the reaction forces on the modified flexure bar mountings and the concomitant structure-borne vibrations, are virtually eliminated.

A PREFERRED EMBODIMENT OF THE PIEZOCERAMIC FLEXBAR

A preferred embodiment of the FLEXBAR is shown in Fig. 5. It is of trilaminar construction; the center lamina of which is a metal bar 13 of generally rectangular cross-section, with a relatively thin center web 14 and enlarged ends 15. Electrical insulation 16 and 17 line the inner sections of the metal bar, forming a top and bottom opening. Two outer laminae 18-A and 18-B consisting of a plurality of piezoceramic blocks with suitable electrodes 19 and assembled with appropriate polarity, are placed in the top and bottom openings. The whole assembly, including the metal bar 13, the insulation 16 and 17, and the piezoceramic blocks 18-A and 18-B are consolidated into a solid composite bar by means of an electrically insulating cement. Electrical leads 20 are connected to the piezoceramic block electrodes 19 with appropriate polarity, with the leads 21-A and 21-B extending out from the inside bottom of the bar. Tuning masses 22 are attached to the bar end sections 15 by means of bolts 23. Metal mounting pins 24 with rubber tubing covers 25 are inserted into nodal holes 26 located on the center line of the bar at the nodal planes 27. In order to minimize tensile strain in the brittle piezoceramic blocks, they are subjected to a precompression mechanical bias during assembly by means of the metal bias-blocks 28 ... said precompression being measured by resistance strain gages 29 cemented to the center-web 14 both top and bottom. Metal-clad plastic plates 30 are cemented to the top and bottom of the bar to enhance its shock resistance. Finally, electrical conductors 20 leading from the piezoceramic blocks are entirely imbedded in high dielectric strength cement in order to avoid electrical breakdown and corona discharge under the high drive voltages.
Three different configurations of mechanical bias blocks were found useful in applying precompression bias to the piezoceramic blocks. The first of these methods is biased on the use of wedges as shown in Fig. 6-A and Fig. 6-B. Here, pairs of wedges 31 and 32 are inserted, top and bottom, at one end of the metal bar 13 between the piezoceramic stacks 18-A and 18-B and both of the shoulders of the enlarged bar end section 15. Electrical insulating pads 17 between the wedge- pairs 31 and 32 and the piezoceramic stacks 18-A and 18-B insulate the stacks from the bar ground potential. Each wedge has one parallel face and one inclined face and all inclined faces have the same incline angle. The wedge-pairs are assembled with the inclined faces mated. More-or-less equal, inward forces are applied along the main axis of the wedge-pairs (at right angle to the main bar axis), forcing the piezoceramic stacks against the shoulders of the enlarged bar end section 15 at the opposite end of the metal bar. This results in tension stress in the bar center web 14 and compression stress in the piezoceramic stacks 18-A and 18-B. The amount of precompressional stress in the piezoceramic stack can be controlled by the incline angle of the wedges, the force applied to the wedges, the cross-sectional area of the center web and the tension modulus of the material of the center web. The strain gages 29 shown in Fig. 5 are used to measure the tension force in the web, which, of course, equals the compressive force in the piezoceramic stack. The whole process is most easily accomplished if the piezoceramic stacks 18-A and 18-B are preassembled with their insulation 16 and 17 cemented in place. The cement is then applied between the center web 14 and the insulating plates 16. The stacks 18-A and 18-B are then placed on the bar and put into compression. The cement joint between the web 14 and the insulating plates 16 is allowed to set up with the stacks under compression, thus avoiding an unwanted shear stress in this cement joint. The protruding end of the wedges can then be cut off along the dotted lines 33.
An alternative means for applying precompression is shown in the sectional sketch of Fig. 7. Here a pair of mechanical bias blocks 34 with tapered holes drilled into each end of the block pair are inserted between the piezoceramic stack 18 (with end insulating pad 17) and the shoulder of the enlarged end section 15 of the bar. The blocks are forced apart by driving two taper-pins 35 into the tapered holes, resulting in precompression of the piezoceramic stack (and tension in the bar center web). In the somewhat similar method of Fig. 8, the tapered holes in the blocks 36 are threaded and tapered, threaded plugs 37 are screwed into the blocks, forcing them apart and, thus, precompressing the piezoceramic stack. As before, the protruding ends of the taper-pins or threaded-plugs can be removed after the inner cement joints have fully set-up.
The FLEXBAR shown in Fig. 5 can be set into flexural vibration by applying an alternating electrical voltage to the terminals 21-A and 21-B. Since the piezoceramic stacks 18-A and 18-B are oppositely polarized, one-half cycle of the resulting alternating current causes the upper stack to expand and the lower stack to contract; and in the next half of the cycle the opposite occurs. This results in the bar being driven in flexural vibration at the frequency of the applied alternating current. The amplitude of vibration is a maximum at the resonant frequency (lowest mode) of the FLEXBAR, which is given by the approximate formular:

where:

f_o =: the resonant frequency of the bar (Hz)
a =: the thickness of the bar (inches)
l =: the nodal length (inches)
c =: effective longitudinal velocity of the bar (in/sec)

FLEXBAR

Brass tuning weights

epoxy plates

OPERATIONAL CHARACTERISTICS OF THE FLEXBAR

Fig. 10 shows a typical measured relative (rms) displacement, in decibels, of the center of the FLEXBAR of Fig. 9-B as a function of frequency. In this case the bar was measured in air and exhibited resonance at the design frequency. The high mechanical Qm ≃ 130 indicates that the bar has very low internal mechanical losses. Fig. 11 shows the measured relative displacement along the same FLEXBAR driven at its resonant frequency. The nodes are well defined and some 60 db below the center deflection. Fig. 12 shows the measured total impedance vs. frequency of the same FLEXBAR with a typical resonance-antiresonance at ∼1 KHz. The next higher mode at ∼2.75 KHz is nearly suppressed, but discernable, and the third mode at ∼5.4 KHz, is also discernable. Above 10 KHz the bar breaks up into a number of complex resonant modes.
One of the remarkable and unique properties of the FLEXBAR is its capability of being mechanically tuned over approximately an octave, as shown in Fig. 13. This also represents experimental data obtained for the FLEXBAR shown in Fig. 9-B. The resonant frequency with no added "tuning" masses is ∼1350 Hz, and this frequency is systematically reduced as mass is added. For a total added mass of 2500 grams (sum of mass at both ends). The resonant frequency is reduced to ∼660 Hz, or approximately 1 octave lower. Also shown in Fig. 13, is the effect of added mass on the location of the nodal points. The effect is relatively small for such a wide range of frequencies representing approximately ± 12,7 mm (± 0.5 inches) from the location for the design frequency. Since the nodal mounting pins 24 of Fig. 5 are decoupled from the vibrating FLEXBAR by means of the compliant rubber sleeve 25, the small movement of the nodal point location has little effect on the performance of the bar. For the design frequency of 1000 Hz, the total added mass is approximately 1200 g, or 600 g on each end. As can be seen from Fig. 14, this wide range of added mass has negligible effect on the electromechanical coupling coefficient of the FLEXBAR.
An important consequence of these unique properties is the fact that production runs of FLEXBARs can be easily all tuned to the same nominal design frequency by adding or subtracting small amounts of mass from the end tuning masses. This results in improved quality control and reduced cost.

A FLEXBAR TRANSDUCER: THE FLEXDUCER

A FLEXBAR sonar transducer is comprised of one or more FLEXBARs, nodally mounted in a suitable water-tight housing, and acoustically coupled to the water through a sound-transparent rubber window. Fig. 15 is a schematic sketch showing the principal parts comprising such a transducer: the cover plate 38 has a bonded sound-transparent rubber window 39 with bolt holes 40; an ensemble of FLEXBARs 41 with nodal mounting pins 42; and a flanged housing 43 with an electrical cable 44. In order to distinguish such a FLEXBAR transducer from one comprised of bender-bar elements, it is named it a "FLEXDUCER", and this terminology will be used throughout the rest of this specification. Fig. 16-A, Fig. 16-B, and Fig. 16-C are, respectively, the top-view, the end-view, and the side-view of a FLEXDUCER module comprised of 5 FLEXBARs of the design shown in Fig. 9-B having element performance characteristics delinated above. Fig. 17-A, Fig. 17-B, and Fig. 17-C are, respectively, the top-view, the side-view, and the end-view of sectional sketches showing certain design details of the FLEXDUCER construction. In this design, the FLEXBARs 41 are mounted by means of their rubber covered nodal pins 42 to mounting lugs 46 rigidly attached (actually cast) to the cover plate 38. Thus, all 5 of the FLEXBARs are preassembled to the cover plate, and the sound-transparent rubber window 39 is then molded to the cover plate and the radiating face of the FLEXBARs. The finished cover plate subassembly, after proper electrical connections are made to the driving cable, is then mounted onto the flange of the housing 43 and secured by bolts 45. An O-ring seal 44 prevents water leakage in the housing.
Fig. 18 shows a conventional equivalent circuit, that represents the response of the FLEXDUCER; the circuit components being defined as follows:

E =: applied voltage
I =: Electrical current
C_b =: Electrical capacitance
1:N =: Electromechanical transfer function
C_m =: Mechanical compliance of the bar between the nodes
M₁ =: Mass of the bar between nodes
M₂ =: Total mass of bar ends beyond nodes
Rm =: Mechanical resistance of the bar
M_r =: Radiation mass
R_r =: Radiation resistance
F =: Force applied to the water load
U =: Mechanical current (velocity)

The FLEXDUCER of Fig. 16-B is intended to be a module of a large, high power plane array with a nominal center frequency of 1 KHz. Since its dimensions (15" x 15") are small compared to the wavelength (λ = 60"), the acoustic power output will be stress limited to ∼600 acoustic watts. Fig. 20 shows the maximum acoustic power output as a function of the number of modules in a rectangular array. The transition from the stress-limited to the field-limited output occurs at approximately 6 modules. For 40 modules, the FLEXDUCER array would be capable of 100 KW of acoustic power output. The mechanical Qm drops from ∼3.5 for a single module to ∼35 for the full array of 40 modules due to the increase in radiation loading.
The importance of the nodal mounting of the FLEXBAR in the FLEXDUCER module and its effectiveness in virtually eliminating structure-borne vibration is demonstrated by the experimental data of Fig. 21. Here, a comparison of housing transmissibility is made between the FLEXBAR module and an equivalent conventional bender-bar module. In this case, the housing transmissibility is defined as the ratio of the vibration amplitude of the bar at its center to the vibration amplitude of the housing resulting from the vibration of the bar, in decibels; i.e., $Transmissibility = 20 log (bar amplitude/housing amplitude)$
. As can be seen, the FLEXBAR module has an average transmissibility of -60 dB over a whole octave from 700 - 1,400 Hz; i.e. the amplitude of vibration of the housing is only 0.1% of that of the FLEXBAR. By contrast, the transmissibility of the bender-bar module is on the average, only -14 dB; i.e. the amplitude of vibration of the housing is 20% of that for the bender-bar. The significance of this difference becomes clear if one considers a large, high-power array capable of an acoustic output of 0.5 megawatts. The back radiation from the FLEXDUCER array would only be of the order of 0.5 acoustic watts; while the bender-bar array would have back radiation of ∼20,000 watts.

MEANS FOR DRIVING PIEZOCERAMIC FLEXBARS

There are e.g. three principal means for electromechanically driving piezoelectric FLEXBARs. In the first of these shown in Fig. 22, the FLEXBAR is comprised of two piezoceramic plates 47 with electrodes 48 on the main faces, and the polarization vector P essentially perpendicular to the principal axis of the bar. Application of an alternating voltage V to the terminals of the bar results in an electric field vector E, either parallel or anti-parallel to the polarization vector. In turn, the electric field, because of the electromechanical coupling, causes an expansion strain +S in the upper plate and a contraction strain -S in the lower plate, both strains being parallel to the main axis of the bar. On the next cycle of the driving voltage, the mechanical strains are reversed and the FLEXBAR is driven into flexural vibration. In this case where the strain is at right angles to the field, the electromechanical coupling coefficient is typically k₃₁ ≃ 0.30.
In the second configuration, shown in Fig. 23, the electromechanical driving elements are two stacks 49 of piezoceramic blocks 50 consolidated with an appropriate cement (e.g. epoxy), and with electrodes 51 so oriented that the electric field E and the mechanical strain S are in the same direction and parallel to the main axis of the bar, as shown. This is the same means for driving the bar also depicted in Fig. 5. In this case the electromechanical coupling coefficient is higher, typically k₃₃ ≃ 0.60.
In the third configuration, shown in Fig. 24, the electromechanical driving elements are two piezoceramic plates 52 with striped-electrodes 53 fused to the ceramic in regularly spaced bands, the plates are polarized parallel to the longitudinal axis of the bar, but in alternating directions as shown. Thus, in this configuration the mechanical strain S and the electric field E are also substantially in the same direction and parallel to the main axis of the bar. However, because of fringing of the electrical field, the electromechanical coupling coefficient is less than that of the second configuration, being typically k_sp ≃ 0.45.

MEANS FOR MECHANICAL TUNING OF FLEXBARS

One of the unique features of a FLEXBAR is the fact that it can be mechanically tuned by varying the amount of the total moment of inertia of the end portions of the bar beyond the nodal lines, symbolically designated as M₂ in the equivalent circuit of Fig. 18. Three means of achieving this have been devised ; viz,: (1) by varying the amount of the added-mass end pieces; (2) by varying the position of a portion of the added-mass end pieces; and (3) by a combination of both (1) and (2). These means for mechanical tuning apply equally well to piezoceramic FLEXBARs and FLEXBARs driven by other means (e.g. electrodynamic drive, variable reluctance drive, etc.).
The mass M₂ can be reduced by simply drilling holes 54 in the added-mass end pieces as shown in Fig. 25-A; or it can be increased by filling the holes with a high density material such as lead 55 as shown in Fig. 25-B. Another way of varying the mass M₂ is shown in Fig. 25-C, where plates 56 are added or removed from the added-mass end pieces. Reducing the added-mass, of course, increases the resonant frequency of the bar; and increasing the added-mass reduces the resonant frequency.
The second means for mechanically tuning a FLEXBAR does not vary the added-mass, but rather moves the centers-of-mass of the end pieces away from, or toward the nodal points. This varies the total moment of inertia (linear plus rotational) of the end-pieces, and changes the resonant frequency accordingly. In Fig. 26-A, for example, slotted plates 57 are bolted in their extreme outward position, which lowers the resonant frequency. In Fig. 26-B, the slotted plates 57 are in their extreme inward position, resulting in a higher resonant frequency. Intermediate positions result in intermediate resonant frequencies.
Another way of varying the moment of inertia of the end-pieces, and thus changing the resonant frequency, is shown in Fig. 26-C. Here threaded tuning-slugs 58 located in the added-masses 59 can be moved outward to lower the frequency, or inward to raise the frequency. The tuning slugs can be locked into position by means of locknuts 60 or set screws 61. The percentage change in frequency can be increased by filling the tuning-slugs with a higher density material such as lead.
Obviously, the resonant frequency of a FLEXBAR can be varied by means of a combination of the above procedures.

MEANS FOR NODAL MOUNTING OF FLEXBARS

Two principal means for nodal mounting of FLEXBARs will be described. For a new bar design, the location of the nodes must be first be determined. This is readily done by driving a prototype FLEXBAR 63 at its lowest resonant mode and locating the nodes 64 by means of a probe accelerometer or phonograph pick-up (Fig. 27-A). Holes are drilled at these nodal locations to accommodate the nodal pins 65 and their compliant elastomer sheath 66 as shown in the cross-sectional Fig. 27-B. Compliant elastomer washers 67 are inserted between the bar and the mountings 68. This combination isolates the FLEXBAR from its mounting and decouples bar vibrations from the mounting structure. An alternate to this method is shown in Fig. 27-C. In this variant integral tabs 69 at the nodal points extend out from the bar 63 and are encased in a compliant elastomer sheath 66. This, together with the compliant elastomer washers 67, serve to isolate the bar from the mounting 68. The vibration isolation of the nodal pins or nodal tabs, by means of compliant members, is an important feature of the "fixed-nodal mounting" since subsequent mechanical tuning and radiation loading can result in small movement of the nodal locations determined from experimental measurements of FLEXBAR vibrations in air. The compliant mounting accommodates to this change.
The second means for nodal mounting of FLEXBARs is called the "auto-nodal mounting" and is shown in section view of Fig. 28. In this case, a flange 70 completely surrounds the FLEXBAR 63 which is encased in a compliant elastomer 71 serving as a sonar window and 72 serving as a compliant mount. The elastomer is bonded to both the flange and to the bar so that the FLEXBAR is essentially "floating" in elastomer. The ends of the bar are recessed with an intervening air space so that their vibration is decoupled from the flange. Under these conditions, the FLEXBAR automatically determines its own nodal location corresponding to a particular radiation loading.

Claims

An underwater acoustic transducer, comprising:
a) a free-free flexure bar (9; 13, 14, 15; 41; 63);

b) means (18, 19, 20; 44; 47, 48; 49, 50, 51; 52, 53) for electromechanically driving said bar in flexural vibration over a band of frequencies having as its central frequency a frequency, substantially corresponding to the lowest free-free flexural mode of said bar;

c) means (2, 5; 24-27; 42; 68, 70) for mounting said flexure bar substantially at the two nodal lines (2, 27) characteristic of the said lowest free-free flexural vibrational mode of the said bar;

d) elastomeric members (66, 67, 72) partially isolating said mountings (68) from the vibration of the said flexure bar (63);

e) means (38, 42, 45, 46) for affixing said flexure bar and its said nodal mountings into a gas-filled water-tight housing (6, 43) in such a manner that the flexure bar can vibrate freely on its nodal mountings without substantial mechanical coupling to said mountings or said housing;

f) means (39) for mechano-acoustically coupling to the water only the central portion (9) of the outer surface of said bar (9; 13-15; 41; 63) lying between said two nodal lines (2, 27) so that when electromechanically driven in flexural vibration, said flexure bar will radiate acoustic energy into the water from said central portion (9);

g) means for allowing those outer portions (8A, 8B; 22) of said flexure bar lying outside of said two nodal lines to vibrate freely in the gas-filled interior of said housing (6, 43) without mechanoacoustic coupling to the water.
The transducer of Claim 1, characterized by comprising a plurality (41) of said free-free flexure bars.
The transducer of Claim 1 or 2, characterized in that the free-free flexure bar comprises two modified end sections (8A, 8B; 22) lying outside of the nodal lines (2, 27) of said flexure bar which are rigidly attached to the central portion of said bar and extend at substantially right angles to and on the opposite side of the central radiating surface of said flexure bar, where said end sections would provide substantially the same total inertia, both translational and rotational, taken about the nodal lines, as would be provided by uniform end sections extending outside of the nodal lines and parallel to the central radiating face of the free-free flexure bar.
The transducer of claim 3, characterized in that the said modified end sections have a portion (12) of their surfaces that are contiguous with the central radiating surface (9) recessed so as to avoid vibrational interference with a transducer cover plate (38).
A vibratile element, suitable for use in a transducer according to one of the preceding claims,
comprising :
a) a free-free flexure bar (9; 13, 14, 15; 41; 63);

b) means (18, 19, 20; 44; 47, 48; 49, 50, 51; 52, 53) for electromechanically driving said bar in flexural vibration over a band of frequencies having as its central frequency a frequency substantially corresponding to the lowest free-free flexural vibrational mode of said bar;

c) means for mounting said flexure bar substantially at the two nodal lines characteristic of said lowest free-free flexural vibrational mode of said bar;

d) elastomeric members (66, 67, 72) partially isolating said mountings from the vibrations of said flexure bar;

e) two modified end sections (8A, 8B; 22) lying outside of the nodal lines (2, 27) of said flexure bar which are rigidly attached to the central portion (9) of said bar and extend at substantially right angles to and on the same side of central portion of said bar; where

f) said end sections (8A, 8B; 22) would provide substantially the same total inertia, both translational and rotational, taken about the nodal lines, as would be provided by uniform end sections extending outside of the nodal lines and parallel to the central portion of said free-free flexure bar.
The vibratile element of claim 5, characterized by means (54 to 61) for changing the mass of said modified end sections (8A, 8B; 22, 59) so as to change the frequency substantially corresponding to the lowest free-free flexural vibrational mode of said bar.
The vibratile element of claim 5, characterized by means (54 to 61) for changing the moment of inertia taken about the nodal lines (2, 27) of said modified end sections (8A, 8B; 22, 59) so as to change the frequency substantially corresponding to the lowest free-free flexural vibrational mode of said bar.
A vibratile element suitable for mounting in an underwater acoustic transducer housing, in particular a transducer according to one of the claims 1 to 4,
comprising :
a) a free-free flexure bar (63) having two modified end sections (8A, 8B, 22) lying outside the two nodal lines (2, 27) characteristic of the lowest free-free flexural vibrational mode of said bar, said end sections being rigidly attached to the central portion (9) of said flexural bar and extending substantially at right angle to and in the same direction from the central portion of said bar, where said end sections would provide substantially the same total inertia, both translational and rotational, take about the nodal lines, as would be provided by uniform end sections extending outside of the nodal lines of an unmodified, uniform free-free flexure bar;

b) means (18, 19, 20; 44; 47, 48; 49, 50, 51; 52, 53) for electromechanically driving said bar in flexural vibration over a band of frequencies having as its central frequency a frequency substantially corresponding to the lowest free-free flexural vibrational mode of the said bar;

c) compliant elastomeric layers (72) between each side of said flexure bar (63) and corresponding parallel mounting structures (70) attached to the said transducer housing, in such a manner that said bar is suspended in said compliant elastomeric material (71, 72) and, when driven, is substantially free to vibrate in flexure, seeking its own nodal lines irrespective of changes in the total inertia of said end sections, or changes in radiation loading; and

d) means (71) for acoustic coupling to the water, only the central face of said bar lying between the nodal lines and opposite to the extension of said modified end sections, leaving the other face of said bar and its said end sections decoupled from the water end and free to vibrate in the air-filled interior of the said transducer housing (43).
An apparatus according to one of the claims 1 to 8, characterized in that the means for electromechanically driving said bar (9; 13, 14, 15; 41; 63) in flexural vibration is a piezoelectric means.
The apparatus of claim 9, characterized in that the piezoelectric means is one of a class of polarized piezoceramics.
The apparatus of claim 9 or 10, characterized in that the piezoelectric means comprise two piezoceramic plates (47) provided with electrodes (48) on the main faces of said plates, whereat the polarization vector extends essentially perpendicular to the principal axis of the bar.
The apparatus of claim 9 or 10, characterized in that the piezoelectric means comprise at least two stacks (49) of piezoceramic blocks (50) with electrodes (51) oriented such that the electrical field between the electrodes and the mechanical strain are in the same direction and parallel to the main axis of the bar.
The apparatus of claim 9 or 10, characterized in that the piezoelectric means are at least two piezoceramic plates (52) with strip-shaped electrodes (53) in regularly spaced bands, the plates are polarized parallel to the longitudinal axis of the bar, but in alternating directions.
An apparatus according to one of the claims 1 to 8, characterized in that the means for electromechanically driving said bar in flexural vibration is a magnetostrictive means.
An apparatus according to one of the claims 1 to 8, characterized in that the means for electromechanically driving said bar in flexural vibration is a magnetic electrodynamic means.
An apparatus according to one of the claims 1 to 8, characterized in that the means for electromechanically driving said bar in flexural vibration is a variable magnetic reluctance means.
The apparatus of claim 10, characterized by means (28; 31, 32; 34, 35; 36, 37) to subject the polarized piezoceramic (18, 18A, 18B) to a substantially permanent precompression mechanical bias in the course of fabrication of the said vibratile element.
The apparatus of claim 17, characterized in that a pair of tapered wedges (31, 32) are the means for obtaining the said mechanical bias.
The apparatus of claim 17, characterized in that a pair of tapered pins (35) and matching blocks (34) are the means for obtaining the said mechanical bias.
The apparatus of claim 17, characterized in that a pair of tapered threaded bolts (37) and matching blocks (36) are the means for obtaining the said mechanical bias.
The apparatus according to one of the preceding claims, characterized by means for mechanically tuning the bar.
The apparatus of claim 21, characterized in that the mass of the end pieces (22) of the bar is changeable.
The apparatus of claim 21, characterized by means for changing the position of the center-of-mass of the end pieces (22).
The apparatus according to one of the preceding claims, characterized in that the bar (63) at each nodal location (64) has a hole for accommodating a nodal mounting pin (65) and a compliant elastomer sheath (66), and a compliant elastomer washer (67) is inserted between the bar and the mounting.
The apparatus according to one of the claims 1 to 23, characterized in that at each nodal point (64) of the bar (63) an integral tab (69) extends out from the bar and is encased in a compliant elastomer sheath (66), which together with a compliant elastomer washer (67) isolates the bar from the mounting (68).
The apparatus according to one of the claims 1 to 23, characterized in that a flange (70) completely surrounds the bar (63), which is encased in a compliant elastomer (72), such that the elastomer is bonded to both the flange and to the bar and the bar is essentially floating on the elastomer.
The apparatus of claim 26, characterized in that the ends of the bar are recessed with an intervening air space for decoupling them from the flange.