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Jun 30, 2018 - J. Acoust. 2012, 36, 285–294. 17. Osborn, J.W.; Wason, C.P.; Mcnary, W.S. Openwork Shell Projector. U.S. Patent US6956792, 18 November.

sensors Article

A Conformal Driving Class IV Flextensional Transducer Tianfang Zhou 1,2,3 , Yu Lan 1,2,3, *, Qicheng Zhang 1 , Jingwen Yuan 1 , Shichang Li 1 and Wei Lu 1,2,3, * 1

2 3

*

College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001, China; [email protected] (T.Z.); [email protected]uk (Q.Z.); [email protected] (J.Y.); [email protected] (S.L.) Acoustic Science and Technology Laboratory, Harbin Engineering University, Harbin 150001, China Key Laboratory of Marine Information Acquisition and Security, Harbin Engineering University, Ministry of Industry and Information Technology, Harbin 150001, China Correspondence: [email protected] (Y.L.); [email protected] (W.L.); Tel.: +86-363-3665-166 (Y.L.); +86-363-3636-884 (W.L.)

Received: 29 May 2018; Accepted: 24 June 2018; Published: 30 June 2018

 

Abstract: Class IV Flextensional Transducers (FTs) are the most popular among various FTs used as low-frequency and high power underwater acoustic sources. However, an undeniable fact exists in Class IV FTs is that the resonance frequency of breathing mode regulator used is fairly raised by its longitudinal driver stacks. In this research, a conformal driving Class IV FT in which the driver stacks are kept conformal with its oval shell was proposed aiming at the limitations of conventional driving Class IV FTs described above. The device exhibits competitive Transmitting Voltage Responses (TVRs) but much lower operation frequencies with respect to conventional driving Class IV FTs, through the designs of conformal and segmentally controlled driver stacks. Geometric parameters analysis was carried out extensively by Finite Element (FE) simulations for the design optimizations and then a conformal driving Class IV FT resonating at 510 Hz (45% approximately lower than that of conventional driving Class IV FT with the same shell geometry) was finalized. Subsequently the conformal driving Class IV was fabricated and tested in the anechoic tank experimentally. Good agreements of both FE predictions and experimental results demonstrate its low-frequency and small-size acoustic performance. Keywords: conformal driving class IV flextensional transducer; low frequency; high power; small size

1. Introduction It is widely known that the low-frequency, small size and high-power underwater transducers exhibit many potential applications in underwater acoustic domain, such as the long-range detection and tracking, marine environmental monitoring and development, as well as the small underwater target platforms (UUV and AUV) [1–4]. In particular, Flextensional Transducers (FTs) are a generic type of low-frequency, small-size and high-power underwater transducers, which make use of the displacement amplification mechanism by transferring the extensional vibrations of the driver stacks to the flexural vibrations of the shell configuration [5–9]. The first FTs were built and tested in 1929 at the Anacostia Naval Research Laboratory (NRL), Washington DC, by Harvey C. Hayes, the Director of the NRL Sound Division [10]. It was until the middle-to-late 1950s the FTs were rebirthed and investigated further in Toulis’ work [11]. In fact, the Toulis’ design is roughly identical to that of Hayes, with the exception that the piezoelectric ceramic driver stacks were used instead of the magnetostriction-driven rods in Hayes’s transducer. There’re two

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other patents in parallel with the inventions of Toulis which are the axisymmetric flying-saucer-shaped FTs proposed by Frank R. Abbott [12] and “dogbone” shell FTs designed by Merchant [13], respectively. Recently most of the efforts about FTs have been concentrated on the broadband operations due to their intrinsic high mechanical quality factors and subsequently narrow bandwidths [14–18]. Porzio [14] invented a slotted cylinder FT which exhibits much broader bandwidth than conventional driving FTs by coupling the low frequency flexural mode and the higher frequency “breathing” mode caused by slotted cylinders. Chen et al. [16] proposed a broadband FT with lengthened major axis by the theory of multiple-mode-coupling. It was shown that the resonance frequencies of the 3 modes of interest (the fundamental mode, the second-order mode and the membrane vibration mode) can be tuned by lengthening the major axis and coupling subsequently to broaden the bandwidth of the transducer. Furthermore, Osborn et al. [17] designed a FT in which the honeycomb structure replaces the solid shells, with the honeycomb providing the same bending stiffness of the solid shells but less weight, therefore an increased operation bandwidth. In order to achieve the low-frequency operation of FTs, additional radiation structures have been assembled to the oval shell for larger radiation areas and larger effective mass subsequently, which can ultimately lead to lower operation frequencies both in Refs. [19,20]. Among the various FTs, Class IV FT is a particular type which shows superior performance in terms of low-frequency and high-power property [21–24]. A Class IV FT currently consists of a shell in the form of elliptical cylinder and active diver stacks inside. Longitudinal vibrations of the driver stack, typically in the form of a bar, can be shifted to a combined flexural vibration mode of the shell which exhibits amplified amplitude motions and decreased resonance frequencies. However, compared with the resonance frequency of the shell itself, a drawback brought by this design is that the resonance frequency of the combined flexural mode is fairly raised by the additional effective stiffness caused by longitudinal driver stack. To solve the above problems, the conformal driving Class IV FT is proposed. This an enhanced type of FT in which the active driver elements are kept conformal and adhered to the oval shell. It is shown by Finite Element (FE) predictions and experimental test that the resonance frequency of the breathing vibration mode of the conformal driving Class IV FT is obviously lower than that of the conventional longitudinal driven FT of the same dimensions. In addition, the methods of segmented driving and phase control are utilized for optimizing the vibrational amplification and subsequently achieving a higher power performance of the transducer. The design of conformal driving Class IV FT is given in Section 2. Parametric analysis by FE simulations and experimental measurements are presented in Sections 3 and 4 respectively, followed by the conclusions eventually. 2. The Design of Conformal Driving Class IV FTs In the conformal driving Class IV FT schematic in Figure 1b, the conformal driver stacks are used instead of the longitudinal driver stacks in conventional driving Class IV FTs plotted by Figure 1a. It is expected that the effective stiffness of the geometry and subsequent vibrational frequency is significantly lowered by the design of conformal driver stacks. Here the conformal driving is defined as a geometric form in which the active driver elements are kept conformal to one or several segments of the shell alternatively. With the conformal driving, more agile and diverse driving algorithms can be adapted to optimize the acoustic performance of FTs. In the following sections, the conformal driving Class IV FT was examined first in regard of its low-frequency performance and then the influences of segmented driving and phase control on its high-power performance. It is critical that the conformal driving in our study is only applicable to the FTs which have cylindrical shells, such as Class IV and VII FTs.

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Figure 1. (a) The structure of conventional driving Class IV FTs; (b) The structure of conformal driving Class IV FTs. Figure The structure conventional driving Class FTs; The structure conformal driving Figure 1. 1. (a)(a) The structure ofof conventional driving Class IVIV FTs; (b)(b) The structure of of conformal driving Class FTs. Class IVIV FTs.

3. Finite Element Analysis of Conformal Driving Class IV FT

3. Finite Element Analysis of Conformal Driving Class IV FT 3. Finite Element 3.1. Modal AnalysisAnalysis of Conformal Driving Class IV FT 3.1. Modal Analysis of the conformal driving Class IV FT is carried out with commercial FE software 3.1. Modal Analysis Modal analysis ANSYS. The geometries of conventional driving Class IV FT and conformal driving ClassFE IV software FT are Modal analysis conformal driving Class carried out with commercial Modal analysis of of thethe conformal driving Class IVIV FTFT is is carried out with commercial FE software shown in Figure 1. Conformal driver stacks (the blue areas) are adhered to the inside of the oval shell ANSYS. The geometries conventional driving Class and conformal driving Class ANSYS. The geometries of of conventional driving Class IVIV FTFT and conformal driving Class IVIV FTFT areare toshown replaceinthe longitudinal driver stacks. Fundamentally, the conformal driver stack is not included Figure Conformal driver stacks (the blue areas) adhered inside oval shell shown in Figure 1. 1. Conformal driver stacks (the blue areas) areare adhered to to thethe inside of of thethe oval shell in Modal analysis and the shell geometries of these two models are basically the same in the process. replace longitudinal driver stacks. Fundamentally, the conformal driver stack not included to to replace thethe longitudinal driver stacks. Fundamentally, the conformal driver stack is is not included The modal shapes ofand 1/4 the model aregeometries presented bythese displacement vector maps in ANSYS Post Processor, Modal analysis shell two models are basically the same the process. in in Modal analysis and the shell geometries ofof these two models are basically the same inin the process. asThe shown in Figure 2. 1/4 model are presented by displacement vector maps in ANSYS Post Processor, modal shapes The modal shapes of of 1/4 model are presented by displacement vector maps in ANSYS Post Processor, shown Figure asas shown in in Figure 2. 2.

(a) (a)

(b) (b)

Figure 2. (a) The first flexural vibration mode shapes of conventional driving Class IV FT; (b) The first Figure 2. (a) The first flexural vibration mode shapes of conventional driving Class IV FT; (b) The first flexural vibration mode shapes of conformal driving Class IV FT. flexural vibration mode shapes of conformal driving Class IV FT. Figure 2. (a) The first flexural vibration mode shapes of conventional driving Class IV FT; (b) The first vibration mode both shapes of conformal driving Class IVnode FT. around the midpoint of the shell Asflexural can been seen from figures, there’s a vibration

As can been seen from both figures, there’s a vibration node around the midpoint of the shell at at which displacement equals to zero and displacements on both sides of node the node are which thethe displacement equals to figures, zero and the the displacements on around both sides of the are shell antiAs can been seen from both there’s a vibration node the midpoint of the at anti-phases. This particular mode is defined as a flexural breathing mode (or fundamental flexural phases. This particular mode is defined as a flexural breathing mode (or fundamental flexural mode). which the displacement equals to zero and the displacements on both sides of the node are antimode). The resonance frequency of conventional driving Class IV FT shown in Figure 2a is 1394.4 Hz, The resonance frequency of conventional driving Class IV FT shown Figure 2a is 1394.4 Hz, while phases. This particular mode is defined as a flexural breathing modein(or fundamental flexural mode). while an identical flexural mode resonating at 492.9 Hz is found in conformal driving Class IV FT. anThe identical flexural mode of resonating at 492.9 Hz Class is found inshown conformal driving Class IVHz, FT. while An resonance frequency conventional driving IV FT in Figure 2a is 1394.4 An obvious decrease (40% approximatively) of breathingmode modefrequency frequencyof ofconformal conformal driving driving Class Class IV obvious decrease (40% approximatively) an identical flexural mode resonating of at breathing 492.9 Hz is found in conformal driving Class IV FT.IV An FT is brought out with respect to that of conventional driving Class IV FT, which will witness conformal FTobvious is brought out with respect to that of conventional driving Class IV FT, which will witness decrease (40% approximatively) of breathing mode frequency of conformal driving Class IV driving FT benefiting morebenefiting in the applicationsinof the low-frequency andof small-size underwater conformal driving applications low-frequency andtransducers. small-size FT is brought out FT with respect tomore that of conventional driving Class IV FT, which will witness underwater transducers. conformal FT benefiting more in the applications of low-frequency and small-size 3.2. Vibrationaldriving Displacement Property Analysis underwater transducers. The overall vibrational displacement property of flexural breathing mode of the conformal driving Class IV FT is shown in the Figure 3. Four vibration nodes and reverse displacement distributions are found as described in Section 3.1.

3.2. Vibrational Displacement Property Analysis 3.2. Vibrational Displacement Property Analysis The overall vibrational displacement property of flexural breathing mode of the conformal The overall vibrational displacement property of flexural breathing mode of the conformal driving Class IV FT is shown in the Figure 3. Four vibration nodes and reverse displacement driving Class IV FT is shown in the Figure 3. Four vibration nodes and reverse displacement distributions are found as described in Section 3.1. distributions found as described in Section 3.1. Sensors 2018, 18,are 2102 4 of 15

Figure Figure 3. 3. The The first first flexural flexural vibration vibration mode mode shapes shapes of conformal driving Class IV FT. Figure 3. The first flexural vibration mode shapes of conformal driving Class IV FT.

In order obtain superior capability acoustic radiation power the transducer, segmented ordertoto toobtain obtaina aasuperior superiorcapability capabilityofof ofacoustic acousticradiation radiationpower powerofof ofthe thetransducer, transducer,segmented segmented InInorder driving and phase control are utilized by taking advantage of the vibrational shape of the breathing drivingand andphase phasecontrol controlare areutilized utilizedbybytaking takingadvantage advantageofofthe thevibrational vibrationalshape shapeofofthe thebreathing breathing driving mode. To make a comparison, two types of conformal driving method are investigated. Four mode. To make a comparison, two types of conformal driving method are investigated. Four conformal mode. To make a comparison, two types of conformal driving method are investigated. Four conformal stacks are assembled in theaccording segments to according to theoflocations of the nodes. The in-phase stacks arestacks assembled in the segments the locations the nodes. The in-phase conformal are assembled in the segments according to the locations of the nodes. The vibrations in-phase vibrations and anti-phase vibrations between the adjacent stacks can be excited by controlling the and anti-phase vibrations between the adjacent stacks can be excited by controlling the driving voltages. vibrations and anti-phase vibrations between the adjacent stacks can be excited by controlling the driving voltages. For convenience, we name them as in-phase conformal driving transducer and antiFor convenience, weconvenience, name them as conformal driving transducer and transducer anti-phase and conformal driving voltages. For wein-phase name them as in-phase conformal driving antiphase conformal driving transducer respectively, as shown in marker Figure 4a,b. Thus, the marker “+” driving transducer respectively, as shown in Figure 4a,b. Thus,in the “+” represents expanding phase conformal driving transducer respectively, as shown Figure 4a,b. Thus, the an marker “+” represents an expanding vibration and marker “-” represents a contracting vibration. vibration an andexpanding marker “-”vibration represents contracting vibration. a contracting vibration. represents anda marker “-” represents

(a) In-phase conformal driving (a) In-phase conformal driving

(b) Anti-phase conformal driving (b) Anti-phase conformal driving

Figure 4. Two types of driving method of conformal driving Class IV FTs. Figure 4. Two types of driving method of conformal driving Class IV FTs. Figure 4. Two types of driving method of conformal driving Class IV FTs.

Similar to to the the acoustic acoustic radiation radiation model model of of pulsating pulsating sphere sphere [25], [25], the the volume volume displacement displacement can can be be Similar Similar to the acoustic radiation model of pulsating sphere [25], the volume displacement can be used here to quantitatively evaluate the sound radiation capacity of conformal driving Class IV FTs, used here to quantitatively evaluate the sound radiation capacity of conformal driving Class IV FTs, used here to quantitatively evaluate the sound radiation capacity of conformal driving Class IV FTs, due to to its its dimension dimension is is much much smaller smaller than than the the wavelength wavelength of of the the sound sound produced produced over over the the frequency frequency due due to its dimension is much smaller than the wavelength of the sound produced over the frequency range of of interest. interest. The The volume volume displacement displacement can can be be defined defined as as an an integral integral of of the the normal normal displacement displacement range range of interest. The volume displacement can be defined as an integral of the normal displacement vector over its radiation surface: Z vector over its radiation surface: vector over its radiation surface: X = Un × h ds (1) X =s0 ∫ 𝑈𝑛 × ℎ 𝑑𝑠 (1) X = ∫ 𝑈𝑛 × ℎ 𝑑𝑠 (1) 𝑠0 where S0 is the integral distance from minor axis𝑠0vertex A to major axis vertex B, Un is the displacement where S0 is the integral distance minorofaxis A to major axis 5.vertex B, Un is the vector normal to the surface and h isfrom the height shell,vertex as illustrated in Figure where S0 is the integral distance from minor axis vertex A to major axis vertex B, Un is the displacement vector normal to the surface and h is the height of shell, as illustrated in Figure 5. displacement vector normal to the surface and h is the height of shell, as illustrated in Figure 5.

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Figure Figure5.5.Schematic Schematicof ofvolume volumedisplacement displacementcalculations. calculations. Figure 5. Schematic of volume displacement calculations.

Consequently, thedistributions distributions ofthe the normaldisplacements displacements along semi-shell semi-shell are obtained obtained by Consequently, Consequently, the the distributions of of the normal normal displacements along along semi-shell are are obtained by by FE simulations, as shown in Figure 6. The values of volume displacements are presented in Figure 7, 7, FE FE simulations, simulations, as as shown shown in in Figure Figure 6. 6. The The values values of volume displacements are presented in Figure Figure under 1 Volt excitation voltage. To be specific, x-axis presents the arc distance from minor axis vertex under Volt excitation excitationvoltage. voltage.ToTo specific, x-axis presents thedistance arc distance from minor axis under 1 Volt be be specific, x-axis presents the arc from minor axis vertex A to the current point X and y-axis is the corresponding accumulation of volume displacement. Note vertex A current to the current point and y-axis is the corresponding accumulation of volume displacement. A to the point X and Xy-axis is the corresponding accumulation of volume displacement. Note that following analysis of volume displacements is under the same resonance frequency for two two Note that following analysis of volume displacements under thesame sameresonance resonance frequency frequency for that following analysis of volume displacements is is under the two driving methods. driving drivingmethods. methods.

Figure 6. The distributions of the normal displacements along semi-shell of transducer. Figure 6. 6. The The distributions distributions of of the the normal normal displacements displacements along along semi-shell semi-shellof of transducer. transducer. Figure

As can be seen from Figure 6, the vibration nodes occur at the same points for both types of As can be seen from Figure 6, the vibration nodes occur at the same points for both types of conformal 0.108 m away from the minor axisoccur vertex. peak of As candriving be seenFTs, from Figure 6, the vibration nodes at However, the same the points fordisplacement both types of conformal driving FTs, 0.108 m away from the minor axis vertex. However, the peak displacement of anti-phasedriving conformal is anfrom orderthe of minor magnitude larger than that ofthe thepeak in-phase one, even conformal FTs,driving 0.108 mFTaway axis vertex. However, displacement anti-phase conformal driving FT is an order of magnitude larger than that of the in-phase one, even of anti-phase conformal driving FT is an order of magnitude larger than that of the in-phase one, though they have identical vibrational modes. though they have identical vibrational modes. Similarly, in have Figure 7, a volume displacement even though they identical vibrational modes. of 1.59 × 10−9 m3 is obtained for the anti-phase FT, Similarly, in Figure 7, a volume displacement of 1.59 × 10−−99 m33 is obtained for the anti-phase FT, −10 m3 volume which is also approximately an order of magnitude larger to the 1.87 × 10anti-phase Similarly, in Figure 7, a volume displacement of 1.59 × with 10 respect m is obtained for the FT, −10 m 3 volume which is also approximately an order of magnitude larger with respect to the 1.87 × 10 − 10 displacement of the in-phase of the results of with Figures 6 and 7 illustrate a larger which is also approximately an one. orderBoth of magnitude larger respect to the 1.87 × 10 m3 acoustic volume displacement of the in-phase one. Both of the results of Figures 6 and 7 illustrate a larger acoustic power. Therefore, a superior acoustic can by segmented driving displacement of the in-phaseperformance one. Both ofof the resultsradiation of Figures 6 be andrealized 7 illustrate a larger acoustic power. Therefore, a superior performance of acoustic radiation can be realized by segmented driving and anti-phase control. power. Therefore, a superior performance of acoustic radiation can be realized by segmented driving and anti-phase control. and anti-phase control.

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Figure 7. The volume displacements along semi-shell of transducer. The volume displacements along semi-shellof oftransducer. transducer. FigureFigure 7. The7.volume displacements along semi-shell

As is known the conventional driving Class IV FT is most applicable due to its effect of As is known the conventional driving Class IV FT is most applicable due to its effect of displacement amplification described above. Displacement ratio is used to indicate indicate the Asdisplacement is known the conventional driving Class IV FTamplification isamplification most applicable due to its effect amplification described above. Displacement ratio is used the of vibrational amplification property of Class IVDisplacement FTs frequently [3,26], isisdefined as the ratioofthe of displacement amplification described above. amplification ratio is usedas tothe indicate vibrational amplification property of Class IV FTs frequently [3,26],which which defined ratio the normal ξ2 at the of minor-axis (point A) to to the displacement the vibrational amplification property ofthe Class IV frequently [3,26], which is defined as the ratio the the displacement normal displacement ξ2 atend end of FTs minor-axis (point A) thenormal normal displacement ξξ1 1atatof the end of major-axis (point B), as B), illustrated in Figure 8. Here FE model examine theof normal displacement ξ2 (point at the endasofillustrated minor-axis (point A)Here toa the normal at the end end of major-axis in Figure 8. a FE modelisdisplacement isperformed performed toξ1examine the of the amplification of conformal driving FT.The The results results show that the effect ofeffect the(point displacement amplification of 8.conformal show that the major-axis B),displacement as illustrated in Figure Here a FE driving model isFT. performed to examine the effect displacement amplification ratio can reach 2.7driving for the conformal drivingFT FTunder under the size displacement amplification ratio can 2.7 for the conformal particular size of the displacement amplification ofreach conformal FT. Thedriving results show thatthe theparticular displacement considered above, which claims thatconformal the conformal driving works equally well in in terms ofofthe considered above, claims that conformal driving FTFT works equally well terms the amplification ratiowhich can reach 2.7 for the driving FT under the particular size considered effect of displacement amplification. effect of displacement above, which claims amplification. that the conformal driving FT works equally well in terms of the effect of displacement amplification.

Figure 8. Displacement amplification motion of Conformal Driving Class IV FT.

Figure8.8.Displacement Displacementamplification amplificationmotion motionofofConformal ConformalDriving DrivingClass ClassIV IVFT. FT. Figure 3.3. Acoustic Radiation Performance Analysis

The FE model in Figure Analysis 9Analysis is constructed in ANSYS to describe the underwater acoustic radiation 3.3. Performance 3.3.Acoustic AcousticRadiation Radiation Performance

of the conformal driving Class IV FT. 1/8 of the geometry is modeled and 3 symmetric conditions are

Theapplied FEmodel model Figure constructed ANSYS describe theunderwater underwater acoustic radiation The FE ininFigure isisconstructed ininANSYS totodescribe the acoustic to improve the99simulation efficiency. No loading is applied on the top surface andradiation bottom theconformal conformal drivingClass Class IVFT. FT.1/8 1/8 thegeometry geometry modeled and33We symmetric conditions are ofofthe IV ofofthe isis modeled symmetric are surface todriving simulate free boundary conditions caused by soft silicon and layer. assign theconditions piezoelectric ceramics by Solid5 element, aluminum shell byloading Silod45,iswater area on by outermost water appliedto toimprove improve thesimulation simulation efficiency. No loading isapplied applied onFluid30 thetop topand surface andbottom bottom applied the efficiency. No the surface and layer by Fluid130 to simulateconditions the nonreflecting boundary. A waterlayer. area of 0.8assign m radius ispiezoelectric constructed surfaceto tosimulate simulate freeboundary boundary conditions caused bysoft softsilicon silicon layer. We assign the piezoelectric surface free caused by We the for far-field conditions. Hexahedral mesh grids are structured with 0.01 m mesh size. The meshing ceramicsby bySolid5 Solid5element, element,aluminum aluminumshell shellby bySilod45, Silod45,water waterarea areaby byFluid30 Fluid30and andoutermost outermost water ceramics water cells add up to 57483. The epoxy adhesive layer, silicon rubber layer, top cover plate and bottom layerby byFluid130 Fluid130totosimulate simulatethe thenonreflecting nonreflectingboundary. boundary.AAwater waterarea areaof of0.8 0.8mmradius radiusisisconstructed constructed layer cover plate used in the fabrication are neglected in FE model. forfar-field far-fieldconditions. conditions.Hexahedral Hexahedralmesh meshgrids gridsare arestructured structuredwith with0.01 0.01m mmesh meshsize. size.The Themeshing meshing for The transmitting Voltage Response (TVR) of transducer is calculated by Harmonic Analysis in cells up 57483. The Theepoxy epoxyadhesive adhesivelayer, layer, silicon rubber layer, cover and bottom cellsadd addANSYS: up to 57483. silicon rubber layer, top top cover plateplate and bottom cover plate plate used used in theinfabrication are neglected in FE in model. cover the fabrication are neglected FE model. TVR=20 × log(p(r) × r / pref) (2) Thetransmitting transmittingVoltage VoltageResponse Response(TVR) (TVR) transducer is calculated Harmonic Analysis The ofof transducer is calculated by by Harmonic Analysis in ANSYS: in ANSYS: TVR = 20 × log(p(r) × r / pref ) (2) TVR=20 × log(p(r) × r / pref) (2)

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where p(r)p(r) is is the far-field generated rmeter meter range the transducer inwhich water, Where far-field pressuregenerated generatedatatat range the transducer in water, which can Where p(r) is the the far-fieldpressure pressure r rmeter range byby theby transducer in water, canwhich canbebe becollected collected in FE model directly. P = 1 µPa/V is reference pressure. Parametric analysis collected in in FE FE model model directly. μPa/V pressure. Parametric analysis is carried directly. PPrefref==11ref μPa/Visisreference reference pressure. Parametric analysis is carried is carried out to investigate theeffect sole effect ofstructural each structural parameter through single-variable method. outto toinvestigate investigate the sole of parameter through single-variable method. The out the effect of each each structural parameter through single-variable method. The structural parameters considered including the ofof major thethe ratio of axis,axis, Thestructural structural parameters considered including the length ofaxis, major axis, themajor-minor of major-minor parameters wewe considered including thelength length major axis, ratio ofratio major-minor the thickness and height for the oval shell, asaswell asasthe number and the height of the conformal axis, the thickness and height oval shell, as well as the number and the height the conformal the thickness and height forfor thethe oval shell, well the number and the height ofof the conformal driver stacks. driver stacks. driver stacks.

Figure elementmodel modelofof transducer in water. Figure9.9.The The finite finite element thethe transducer in water. Figure 9. The finite element model of the transducer in water. The influence of the ratio of major-minor axis under a constant length of major axis was

The influence of the ratio of major-minor axis under a constant length of major axis was investigated first. TVRs are plotted in Figure 10, from under 300 Hz atoconstant 800 Hz. 5length curvesofwith different was The influence of the of major-minor major investigated first. TVRs are ratio plotted in Figure 10,axis from 300 Hz to 800 Hz. 5 curves withaxis different markers represent the TVRs under various ratios of major-minor axis. On can note that the first-order investigated first. TVRs are plotted in Figure 10, from 300 Hz to 800 Hz. 5 curves with different markers represent the TVRs various major-minor axis. ratio On can note that resonance frequency (the under peak in curves)ratios rises of with the increasing from 1.25 to the 2.5 first-order and markersfrequency represent (the the TVRs under various ratios ofthe major-minor axis. On can1.25 note that the first-order resonance peak in curves) rises with increasing ratio from to 2.5 and approaches to a constant when the ratio reaches 2.5. Similar variation patterns are found forapproaches TVR resonance frequency (the peak in curves) rises with the increasing ratio from 1.25 to 2.5 and to a values constant when the ratio reaches 2.5. variation patterns are found TVR values at the resonance frequencies. TheSimilar variations of resonance frequency are for attributed to the at the approaches to a constant when the ratio reaches 2.5. Similar variation patterns are found for TVR resonance frequencies. The variations resonance frequency attributed to by theaincrease of effective increase of effective stiffness and the of decrease of effective massare of the FT caused shorter minor values at the resonance frequencies. The variations of resonance frequency are attributed to the axis. As forthe thedecrease variationsof of effective TVRs, a reduced region of anti-phase subsequent greater acoustic stiffness and mass of the FT caused byand a shorter minor axis. As for the increase of effective stiffness andwith the decrease ofmovements effective mass of the FT axis caused byshorter a shorter minor radiations (or TVR) are obtained the node’s toward major for a minor variations of TVRs, a reduced region of anti-phase and subsequent greater acoustic radiations (or TVR) axis. As for the variations of TVRs, a reduced region of anti-phase and subsequent greater acoustic axis. Fromwith another point of view, a higher resonance frequency represents a larger are obtained the node’s movements toward major axis for a shorter minor axis. radiation From another radiations TVR) areradiation obtainedarea with thetherefore node’s movements toward major performance. axis for a shorter minor resistance (or on the same and a greater acoustic radiation point view, another a higherpoint resonance frequency larger radiation resistance the same axis.of From of view, a higherrepresents resonance afrequency represents a largeronradiation radiation area and therefore a greater acoustic radiation performance. resistance on the same radiation area and therefore a greater acoustic radiation performance.

Figure 10. Influence of the ratio of major-minor axis on the TVR.

Figure Influenceofofthe theratio ratioof of major-minor major-minor axis Figure 10.10.Influence axis on onthe theTVR. TVR.

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Figure 11 presents the numerically simulated TVRs for the conformal driving FTs with various Figure 11 presents the numerically simulated TVRs for the conformal driving FTs with various Figure 11 presents the numerically simulated for the FTsfrequency with various shell thicknesses. An obvious variation pattern wasTVRs seen that the conformal first-order driving resonance and shell thicknesses. An obvious variation pattern was seen that the first-order resonance frequency and shell thicknesses. An obvious variation pattern was seen that the first-order resonance frequency and the corresponding TVR go up along with the increase of shell thickness. It can be explained simply the corresponding TVR go up along with the increase of shell thickness. It can be explained simply the TVR goauplarger alongeffective with the increase shelltherefore thickness.a Ithigher can be resonance explained simply that thatcorresponding a thicker shell has stiffnessofand frequency, that a thicker shell has a larger effective stiffness and therefore a higher resonance frequency, asubsequently thicker shell ahas a larger effective stiffness and therefore a higher resonance frequency, subsequently larger radiation resistance and higher TVR under unchanged radiation areas. subsequently a larger radiation resistance and higher TVR under unchanged radiation areas. a larger radiation resistance and higher TVR under unchanged radiation areas.

Figure Influence of of the Figure 11. 11. Influence the shell shell thickness thickness on on the the TVR. TVR. Figure 11. Influence of the shell thickness on the TVR.

and 13, 13, the the simulation simulation shows that both the heights of oval shell and driver stacks Figures12 12and and InInFigures 13, the simulation shows that both the heights of oval shell and driver stacks acoustic radiation performance. Without loss of of conformal driving FT make little influence on its acoustic of conformal driving FT make little influence on its acoustic radiation performance. Without loss of generality, the theresonance resonancefrequency frequencygoes goesup up withthe the heightofofshell shell and goes down with the height generality, generality, the resonance frequency goes up with with the height height of shelland andgoes goesdown downwith withthe theheight heightof of driver stacks. While the TVRs hold steady with the height of and shellincrease and increase slightly with the driver stacks. While the TVRs hold steady with the height of shell slightly with the height of driver stacks. While the TVRs hold steady with the height of shell and increase slightly with the height of stacks. driver stacks. of driver height of driver stacks.

Figure 12. Influence of the Shell height on the TVR. Figure Figure12. 12.Influence Influenceofofthe theShell Shellheight heighton onthe theTVR. TVR.

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Figure 13. Influence of the driver stacks height on the TVR. Figure 13. 13. Influence Influence of of the the driver driver stacks stacks height height on on the the TVR. TVR. Figure

At last, last, the the ratios ratios of the the number of of ceramics in in long and and short arc arc piezoelectric ceramic ceramic stack are are At At the ratios of of the number number of ceramics ceramics in long long and short short arc piezoelectric piezoelectric ceramic stack stack are considered, while the number of ceramic pieces in short arc stack is fixed. According to the results considered, considered, while while the the number number of of ceramic ceramic pieces pieces in in short short arc arc stack stack is is fixed. fixed. According According to to the the results results plotted in Figure 14, no effect has been found from the ratios on the resonance frequency, while an an plotted plotted in in Figure Figure 14, 14, no no effect effect has has been been found found from from the the ratios ratios on on the the resonance resonance frequency, frequency, while while an increase of TVRs can be seen in the case of more piezoelectric ceramics in long arc stacks. Therefore, increase increase of of TVRs TVRs can can be be seen seen in in the the case case of of more more piezoelectric piezoelectric ceramics ceramics in in long long arc arc stacks. stacks.Therefore, Therefore, for a greater acoustic radiation performance, more ceramics are assembled as possible in long long arc for for a greater acoustic acoustic radiation radiation performance, performance, more more ceramics ceramics are are assembled assembled as as possible possible in in long arc arc stacks in in the fabrication fabrication process. process. stacks stacks in the the

Figure 14. Influence of the ratios of ceramics’ number in long and short arc stacks on the TVR. Figure 14. 14. Influence Influence of of the the ratios ratios of of ceramics’ ceramics’ number number in in long long and and short short arc arc stacks stacks on on the the TVR. TVR. Figure

The analysis analysis of structural structural parameters above above gives aa way way to to determine determine the the accurate accurate geometry geometry of of The The analysis of of structuralparameters parameters abovegives gives a way to determine the accurate geometry the conformal driving Class IV FT with a view to obtain an optimal performance. Generally, the the conformal driving Class IV FT withwith a view to obtain an optimal performance. Generally, the of the conformal driving Class IV FT a view to obtain an optimal performance. Generally, major-minor axis axis ratio ratio and and shell shell thickness thickness have have greater greater impact impact on on the the in-water in-water resonance resonance frequency frequency major-minor the major-minor axis ratio and shell thickness have greater impact on the in-water resonance frequency of the the transducer and and therefore are are treated treated as as major major adjustable adjustable factors. factors. While While the the heights heights of of oval oval shell shell of of thetransducer transducer andtherefore therefore are treated as major adjustable factors. While the heights of oval and driver driver stacks stacks make make aa lesser lesser influence influence on on resonance resonance frequency frequency and and are are used used for for fine fine tuning. tuning. The The and shell and driver stacks make a lesser influence on resonance frequency and are used for fine tuning. in-water TVR is expected to be modified by the shell height and the numbers of piezoelectric ceramics in-water TVR is expected to be modified by the shell height the numbers of piezoelectric ceramics The in-water TVR is expected to be modified by the shelland height and the numbers of piezoelectric in long and short arc stacks. Attention should be paid to the fact that a larger major-minor axis ratio in long and arc stacks. Attention should beshould paid tobe thepaid factto that larger major-minor axis ratio ceramics in short long and short arc stacks. Attention theafact that a larger major-minor causes aa higher higher in-water resonance resonance frequency frequency for for conformal conformal driving driving FT, while while conventional conventional driving driving causes axis ratio causesin-water a higher in-water resonance frequency for conformalFT, driving FT, while conventional FTs take the opposite tack. It is an outstanding point that makes the conformal driving Class IV FT FT FTs take the opposite tack. It is an outstanding point that makes the conformal driving Class IV preferable candidates for regular-geometry, small-size and high-power acoustic sources. preferable candidates for regular-geometry, small-size and high-power acoustic sources.

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Table 1. Structural sizes of Conformal Driving Class IV FT. Sensors 2018, 18, 2102

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Parameter Value Parameter Value Length of major axis Height of the piezoelectric 300 mm 80 mm driving FTs take tack. It is an outstanding point that makes ofthe theopposite shell ceramic stack the conformal driving Class IV FT preferable candidates forthe regular-geometry, small-size high-power acoustic sources. Length of minor axis of Thicknessand of the piezoelectric 140 mm 7 mm shell ceramic stack Table 1.of Structural sizes of Conformal Driving FT. The average thickness Number ofClass LongIVarc 10 mm 14 pieces the shell piezoelectric ceramic stack Parameter Value Parameter Value Number of Short arc Shell height 120 mm 42 pieces Length of major axis of the shell 300 mm Height of the piezoelectric 80 mm piezoelectric ceramicceramic stack stack Length of minor axis of the shell 140 mm Thickness of the piezoelectric ceramic stack Number of Long arc piezoelectric ceramic stack The average thickness of the shell 10 mm Table 2. 120 Structural of conventional Class IV FT. ceramic stack Shell height mm sizes Number of Short arc piezoelectric

Parameter

Value

Parameter

Length of major axisTable 2. Structural sizes of conventional Class IV FT.

300 mm of the shell Parameter Value Length of minor axis 140 Length of major axis of the shell 300mm mm of the shell Length minor axis of the shell 140 mm Theofaverage thickness 10 mm the shell The averageofthickness of the shell 10 mm

Shell height Parameter

7 mm 14 pieces 42 pieces

Value 120 mm Value

piezoelectric 182 mm (L) × 30 mm Shell height mm ceramic stack (W) × 80120 mm(H) 182 mm (L) × 30 mm (W) piezoelectric ceramic stack Number of piezoelectric 80 mm (H) 52×pieces ceramic stackceramic stack Number of piezoelectric 52 pieces

A particular particular conformal investigated based on on the the analysis above. The A conformal driving drivingClass ClassIV IVFTFTwas was investigated based analysis above. structural parameters of the transducer are listed in Table 1. The in-water Admittance vs Frequency The structural parameters of the transducer are listed in Table 1. The in-water Admittance vs Frequency plotofofFTFT obtained by simulations FE simulations is shown in Figure 15a.beItseen canthat be seen that the resonance breathing plot obtained by FE is shown in Figure 15a. It can the breathing resonance reaches 510conductance Hz and the conductance value is 0.8 mS. As comparisons, reaches 510 Hz and the value wherein is 0.8 mS.wherein As comparisons, a conventional Class IVa conventional Class IV FT (10.4 kg in weight in simulations) of same dimensions is examined, whose FT (10.4 kg in weight in simulations) of same dimensions is examined, whose structural parameters structural parameters are list in Table 2. Theisresonance frequency is 940in-water Hz and is conductance in-water are list in Table 2. The resonance frequency 940 Hz and conductance 1 mS, as illustrated is 1 mS, as illustrated in Figure 15b. in Figure 15b.

(a) Conformal driving Class IV flextensional transducer Figure 15. Cont.

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(b) Conventional Class IV flextensional transducer (b) Conventional Class IV flextensional transducer Figure 15. 15. The The admittance admittance curves curves of of two two types types of of Class Class IV IV FT FT in in water. water. Figure Figure 15. The admittance curves of two types of Class IV FT in water.

The in-water TVRs of two types of Class IV FTs are plotted in Figure 16, wherein a maximum TheThe in-water TVRs of two types of Class IV FTs in Figure 16, wherein a maximum value in-water TVRs of two types of Class IV are FTsplotted are plotted in Figure 16, wherein a maximum value of 137.5 dB at resonance frequency 510 Hz for conformal driving Class IV FT is presented by valuedB ofat137.5 dB at resonance Hz for conformal driving Class IV FT is presented by of 137.5 resonance frequencyfrequency 510 Hz for510 conformal driving Class IV FT is presented by blue solid blue solid line, in comparison with the conventional one of same shell geometry (red dotted line) solid line, inwith comparison with the conventional same shell geometry line,blue in comparison the conventional one of same one shellofgeometry (red dotted (red line)dotted whoseline) peak whose peak TVR is is 136 dB locating atat940 The significant fall of of resonant resonant frequency frequency(45% (45% TVR 940Hz. Hz. significant fall TVRwhose is 136 peak dB locating at136 940dB Hz.locating The significant fallThe of resonant frequency (45% approximately) and approximately) and slight change ofofTVR for conformal driving Class IV IV FT FT demonstrate demonstrateitsits approximately) and change TVR forIV conformal drivingitsClass slight change of TVR forslight conformal driving Class FT demonstrate advantages in low-frequency advantages in low-frequency underwater advantages in low-frequency underwaterapplications. applications. underwater applications.

Figure TVRs the conformaland andconventional conventional driving driving Class Figure 16.16. TVRs ofof the conformal Class IV IV FT. FT. Figure 16. TVRs of the conformal and conventional driving Class IV FT.

4. Fabrication and In-Water Testing of Conformal Class IV FT 4. 4. Fabrication Fabrication and and In-Water In-WaterTesting Testingof ofConformal ConformalClass ClassIV IVFT FT A conformal driving Class IV FT schematic in Figure 17 was fabricated based on the FE A driving Class IV schematic in 17 fabricated based on A conformal conformal driving IV FT FT schematic in isFigure Figure 17 was was basedarc-shaped on the the FE FE optimization above. The Class conformal driver element composed of 4fabricated sets of spliced optimization above. The conformal driver element is composed of 4 sets of spliced arc-shaped optimization above. The conformal driver element is composed of 4 sets of spliced arc-shaped piezoelectric stacks, adhering to the inside of the shell. The arc-shaped piezoelectric ceramics are piezoelectric stacks, adhering to the of shell. arc-shaped piezoelectric ceramics are piezoelectric stacks, by adhering toTech. the inside inside of the the shell. The The arc-shaped piezoelectric are PZT4 customized Haisheng Company (Yichang, China) [27] and the oval shell isceramics aluminum. PZT4 customized by Haisheng Tech. Company (Yichang, China) [27] and the oval shell is aluminum. PZT4 byclamped Haisheng Company (Yichang, China) [27] and the shell is aluminum. Thecustomized oval shell is byTech. the top and bottom cover plate and jointed by oval silicon rubber gaskets The oval is by and bottom cover silicon an air backing geometry. The driver stacks are plate pre-stressed by theby oval shell rubber and the gaskets epoxy Theforming oval shell shell is clamped clamped by the the top top and bottom cover plate and and jointed jointed by silicon rubber gaskets forming an air backing geometry. The driver stacks are pre-stressed by the oval shell and the glass layers attached geometry. to the stacks are used stacks for higher mechanical strength and shell electric insulation. forming an air backing The driver are pre-stressed by the oval and the epoxy epoxy glass layers attached to the stacks are used for higher mechanical strength and electric insulation. Materials properties components arefor listed in Appendix The dimensions of conformal glass layers attached to of theallstacks are used higher mechanicalA.strength and electric insulation. Materials ofof allall components listed in Appendix A. 0.15 TheA. dimensions of conformal driving drivingproperties Class IV FT finalized are 0.33are m are long, 0.17 minwide and m high dimensions and 9.2 kg in of weight. Materials properties components listed Appendix The conformal Class IV Class FT finalized are 0.33 m m wide 0.15 and m high 9.2 kg in 9.2 weight. driving IV FT finalized arelong, 0.33 0.17 m long, 0.17and m wide 0.15and m high and kg in weight.

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(a) Arc ceramic stacks

(b) Shell and Ceramic Stack

(c) Encapsulated

Arc ceramic stacks (b) Shell and Ceramic Stack (c) Encapsulated Figure 17. 17.(a) Photographs ofthe the Conformal Conformal Driving Class IV IV FT at at different different stages of of assembly. assembly. Figure Photographs of Driving Class FT stages (a) Arc ceramic stacks (b) Shell and Ceramic Stack (c) Encapsulated Figure 17. Photographs of the Conformal Driving Class IV FT at different stages of assembly.

The transducer 10 10 m)m) in in KeyKey Laboratory of transducer is is tested tested in in the the anechoic anechoic tank tank(25 (25mm××1515mm× × Laboratory Figure 17. Photographs of the Conformal Driving Class IV FT at different stages of assembly. underwater acoustic science and technology, Harbin Engineering University, Harbin, China. The of underwater acoustic science and technology, Harbin Engineering University, Harbin, China. The transducer is tested in the anechoic tank (25 m × 15 m × 10 m) in Key Laboratory of diagram of The theoftransducer testing system isand presented in Figure 18. aChina. depth underwater acoustic science Harbin Engineering University, Harbin, The diagram the testing isthe presented in Figure The transducer is at tested at The aof depth is system tested intechnology, anechoic tank (25The m18. ×transducer 15 m × 10 is m)tested in Key Laboratory of4 m diagram theacoustic testing presented Figure 18. The transducer is tested at atodepth ofto 4far-field m underwater. Aofdistance of system 1.2 mofisisand set between the transducer and theUniversity, hydrophone ensure underwater science technology, Harbin Engineering Harbin, China. The of 4 m underwater. A distance 1.2 m is setin between the transducer and the hydrophone ensure underwater. A distance of 1.2 m is set between the transducer and the hydrophone to ensure far-field diagram of the testing system is presented in Figure 18. The transducer is tested at a depth of 4 conditions. CW pulse signal is chosen as excitation to reduce sound reflections from the sidewalls of far-field conditions. CW pulse signal is chosen as excitation to reduce sound reflections frommthe conditions. CW pulse signal is chosen as excitation to reduce sound reflections from the sidewalls of underwater. A distance of 1.2 m is set between the transducer and the hydrophone to ensure far-field tank. In-water admittance are presented in presented Figure 19.in The resonance frequency is frequency 520 Hz and sidewalls of tank. In-watercurves admittance curves are Figure 19. The resonance is tank. In-waterCW admittance curves are mS. presented in Figure 19. The resonance frequency is 520 Hz andof pulse signal chosen as excitation to reduce sound reflections from the sidewalls the conductance isis0.62 520 corresponding Hzconditions. and the corresponding conductance is 0.62 mS. the corresponding conductance is 0.62 tank. In-water admittance curves aremS. presented in Figure 19. The resonance frequency is 520 Hz and the corresponding conductance is 0.62 mS. AFG3022B/TEK TDS1001B-SC/TEK AFG3022B/TEK Signal Source

Signal Source AFG3022B/TEK Signal Source JYH2000A JYH2000A Power Amplifier Power Amplifier JYH2000A Power Amplifier

TDS1001B-SC/TEK Digital Oscilloscope

Digital Oscilloscope TDS1001B-SC/TEK Digital Oscilloscope NF3628 NF3628 Ampli-Filter Ampli-Filter NF3628 Ampli-Filter

1.2m 1.2m 1.2m

4m 4m 4m

Transducer

Transducer

Transducer

B&K 8105 B&K 8105 Hydrophone B&K 8105 Hydrophone Hydrophone

Figure 18. Diagram of testing system.

Figure 18. Diagram of testing system. Figure 18. Diagram of of testing Figure 18. Diagram testingsystem. system.

Figure 19. Admittance curves of conformal driving transducers in water.

FigureFigure 19. Admittance curves of conformal inwater. water. 19. Admittance curves of conformaldriving driving transducers transducers in

Figure 19. Admittance curves of conformal driving transducers in water.

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Figure 20 shows both the TVR measured experimentally (red solid line) and TVR predicted by FE simulations (blue dotted line) of the transducer. The comparisons between them are listed Figure 20 shows both the TVR measured experimentally (red solid line) and TVR predicted by FE in Table 3. Both of them are in good agreement in terms of resonance frequencies, while the little simulations (blue dotted line) of the transducer. The comparisons between them are listed in Table 3. discrepancies of TVRs and conductance can be explained by the insufficient bonding strength, Both of them are in good agreement in terms of resonance frequencies, while the little discrepancies which is caused by unmatched curvature radius between the driver stacks and oval shell in the of TVRs and conductance can be explained by the insufficient bonding strength, which is caused by fabrication process. unmatched curvature radius between the driver stacks and oval shell in the fabrication process.

Figure 20.20. The transmitting voltage response curves of of thethe transducer in in water. Figure The transmitting voltage response curves transducer water. Table 3. Comparisons of of predicted values to to those measured onon thethe prototype. Table 3. Comparisons predicted values those measured prototype.

Resonance Conductance of of Resonance Frequency Conductance Maximum Value Maximum Value Frequency the Resonance in Water/Hz the Resonance /mS of TVR/dB of TVR/dB in Water/Hz /mS 0.80 Ansys model 510 [email protected] Hz Ansys model 510 520 0.80 0.62 [email protected] Hz Hz Experimental [email protected] Difference:Experimental model vs. experimental 10 −2.1 520 0.62 −0.18 [email protected] Hz Difference: model 10 −0.18 −2.1 vs. experimental 5. Conclusions Item Item

A new type of Class IV FT, conformal driving FT has been proposed as a means to improve the 5. Conclusions low-frequency performance of conventional FTs. In particular, a transducer resonating at 520 Hz A new135.4 typedB of TVR Classwas IV FT, conformal FT has been proposed based as a means improve the and owning fabricated anddriving experimentally characterized on FEto simulations. low-frequency performance of conventional FTs. In particular, a transducer resonating atfrequency 520 Hz and Both FE predictions and experimental testing prove that a significant decrease of resonance owning 135.4 dB TVR was fabricated and experimentally characterized based on FE simulations. Both and almost unaffected TVRs can be obtained by the design of conformal driving. It provides the FE predictions and experimental testing prove that aapplications significant decrease of resonance frequency and conformal driving Class IV FTs with many potential as low-frequency, small-size and almost unaffected TVRs can be obtained by the design conformal driving. It provides high-power underwater acoustic sources. Several specificofconclusions are summarized as the the conformal follows: driving Class IV FTs with many potential applications as low-frequency, small-size and high-power 1. underwater The conformal driving is proposed as a new type of driving geometry, which can significantly acoustic sources. Several specific conclusions are summarized as the follows: lower the resonance frequency of Class IV FT and enrich its structural design diversity. conformal driving proposed control as a new of driving geometry,driving which Class can significantly 2. 1. The Segmented driving andisanti-phase aretype utilized to the conformal IV FT by lower the resonance frequency of Class IV FT and enrich its structural design diversity. matching the vibrational shape and displacement nodes of the oval shell, which can maintain 2. Segmented driving and anti-phase control areinutilized driving Class IV FTofby the high-power operation of the transducer paralleltotothe theconformal displacement amplification matching the vibrational shape and displacement nodes of the oval shell, which can maintain conventional FT. the high-power operation of the transducer in parallel to the displacement amplification 3. 45% decrease of resonance frequency of conformal driving Class IV FT is presented with the shell of conventional FT. geometry unchanged both by FE predictions and experimental measurements. 3. 45% decrease of resonance frequency of conformal driving Class IV FT is presented with the shell Last but notunchanged least, deeply analyzing and mining theexperimental superiority of conformal driving Class IV geometry both by FE predictions and measurements. FT are supposed to be done in further work. There are some fabrication technologies to be improved, Last but not least, deeply analyzing and mining the superiority of conformal driving Class IV such as the precision controls of the conformal driver stacks, the pre-stressing process and so forth. FT are supposed to be done in further work. There are some fabrication technologies to be improved, such as the precision controls of the conformal driver stacks, the pre-stressing process and so forth.

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Author Contributions: Transducer structure design, experiment organization and manuscript drafting by the author T.Z.; Funding support by Y.L.; Fabrication process design and processing of the transducer by J.Y. and S.L.; Data collection and analysis by W.L.; Review and edition of the manuscript by Q.Z. Funding: This research was funded by National Natural Science Foundation of China grant number 11374073. Conflicts of Interest: The authors declare no conflict of interest.

Appendix A Material properties 1. Aluminum: Density: 2790 kg/m3 , Young’s modulus: 71.5 GPa, Poisson’s ratio: 0.34. 2. Silicon rubber: Density: 1094 kg/m3 , Young’s modulus: 311 MPa, Poisson’s ratio: 0.48. 3. Epoxy resin: Density: 1250 kg/m3 , Young’s modulus: 3.6 GPa, Poisson’s ratio: 0.35. 4. Piezoelectric ceramic (PZT-4): Table A1. Material properties of piezoelectric ceramic (PZT-4). C11 E N/m2 )

(1010

C12 E N/m2 )

(1010

C13 E N/m2 )

(1010

C33 E N/m2 )

(1010

C44 E N/m2 )

(1010

C66 E N/m2 )

(1010

13.9

7.78

7.43

11.5

2.56

3.06

Density (kg/m3 )

εs11 /ε0

εs33 /ε0

e31 (C/m2 )

e33 (C/m2 )

e15 (C/m2 )

7500

730

635

−5.2

15.1

12.7

References 1. 2. 3. 4. 5. 6.

7. 8. 9. 10. 11. 12. 13. 14. 15.

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