sensors Article
Finite Element Calculation with Experimental Verification for a Free-Flooded Transducer Based on Fluid Cavity Structure Zhengyao He *, Geng Chen, Yun Wang, Kan Zhang and Wenqiang Tian School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710072, China;
[email protected] (G.C.);
[email protected] (Y.W.);
[email protected] (K.Z.);
[email protected] (W.T.) * Correspondence:
[email protected]; Tel.: +86-137-5994-4527 Received: 16 August 2018; Accepted: 15 September 2018; Published: 17 September 2018
Abstract: A free-flooded transducer that couples the vibration of a longitudinal vibration transducer and the fluid cavity of an aluminum ring was investigated. Given the transducer is based on a fluid cavity structure and has no air cavity, it can resist high hydrostatic pressure when working underwater, which is suitable for application in the deep sea. At first, the structure and working principle of the transducer were introduced. Then, the axisymmetric finite element model of the transducer was established; and the transmitting voltage response, admittance, and radiation directivity of the transducer were simulated using the finite element method. According to the size of the finite element model, a prototype of the transducer was designed and fabricated, and the electro-acoustic performance of the prototype was measured in an anechoic water tank. The experimental results were consistent with the simulation results and showed a good performance of the transducer. Finally, the improvement of the radiation directivity of the transducer by the optimal design of the free-flooded aluminum ring was obtained using the finite element method and verified by experiments. Keywords: free-flooded transducer; fluid cavity structure; finite element model; acoustic radiation
1. Introduction Since ocean exploration is developing towards the deep sea, underwater acoustic transducers require the performance of low frequency and high power in deepwater. The free-flooded structural transducers have good performance in deepwater, with low resonant frequency and high transmitting response [1]. Piezoelectric ceramic rings and tubes are often applied as deepwater transducers, because their characteristics are essentially independent of depth [2–4]. Free-flooded ring transducers composed of piezoelectric ceramic rings are studied [2,3]. A deepwater tube transducer, which transmits signals by mechanically tuning a resonator tube is researched [4]. The Helmholtz resonant transducers are studied for their high-power deepwater use [5–7]. This paper investigated a transducer with a free-flooded structure that couples the vibration of a longitudinal vibration transducer and the fluid cavity of an aluminum ring, which is suitable for application in the deep sea. It can be used in deepwater sonar detection, deepwater acoustic communication, and sound propagation characteristics research in deep sea, etc. The finite element method is a modeling and analysis method of transducers commonly used in recent years. It uses a series of discrete units to represent and model the transducer structure and fluid domain, as such its outstanding advantage is that it can adapt to complex conditions, such as irregular boundary shapes, inhomogeneous materials, and anisotropy; and can perform
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and calculation on transducers of complex structure [8–10]. Using the finite element method to model the easily calculate the resonant frequency, observe displacement modeling andtransducer calculationwe on can transducers of complex structure [8–10]. Using the finite the element method distribution of the transducer at resonance, and obtain the admittance curve, transmitting voltage to model the transducer we can easily calculate the resonant frequency, observe the displacement response curves, and directivity pattern of the transducer [10]. It can also be used to optimize the distribution of the transducer at resonance, and obtain the admittance curve, transmitting voltage structure of transducers. The acoustic radiation characteristics of free‐flooded ring transducers are response curves, and directivity pattern of the transducer [10]. It can also be used to optimize the calculated using the finite element method [2]. The Class IV flextensional transducer is modeled and structure of transducers. The acoustic radiation characteristics of free-flooded ring transducers are calculated using the finite element method ANSYS The Class III barrel‐stave flextensional calculated using the finite element method [2].in The Class [10]. IV flextensional transducer is modeled and transducer coupling the fundamental flexural and longitudinal modes of vibration flextensional is calculated calculated using the finite element method in ANSYS [10]. The Class III barrel-stave using the finite element analysis techniques [11]. In this paper, the finite element method was used transducer coupling the fundamental flexural and longitudinal modes of vibration is calculated using to finite model and calculate the free‐flooded based on fluid cavity the the element analysis techniques [11]. Intransducer this paper, the finite element methodstructure, was usedwhere to model influence of the free‐flooded aluminum ring on radiation directivity is analyzed, the size of the and calculate the free-flooded transducer based on fluid cavity structure, where the influence of the transducer aluminum is optimally designed, and directivity the performance is verified by ofexperiments in is the anechoic free-flooded ring on radiation is analyzed, the size the transducer optimally water tank. designed, and the performance is verified by experiments in the anechoic water tank. 2.2. Structure of the Transducer Structure of the Transducer
The structure of the free‐flooded transducer based on fluid cavity structure is shown in Figure 1. The structure of the free-flooded transducer based on fluid cavity structure is shown in Figure 1. This kind of transducer is free‐flooded with a fluid cavity, which has no air cavity. It can resist high This kind of transducer is free-flooded with a fluid cavity, which has no air cavity. It can resist high hydrostatic pressure when working underwater, which is suitable for application in the deep sea. hydrostatic pressure when working underwater, which is suitable for application in the deep sea. The transducer couples the vibration of a longitudinal vibration transducer and the fluid cavity of an The transducer couples the vibration of a longitudinal vibration transducer and the fluid cavity of an aluminum ring. longitudinal vibration transducer is using stacked using of24 pieces of PZT‐4 aluminum ring. TheThe longitudinal vibration transducer is stacked 24 pieces PZT-4 piezoelectric piezoelectric ceramic. The two head mass, which are made of stainless steel material, are an inverted ceramic. The two head mass, which are made of stainless steel material, are an inverted frustum a longitudinal cone. The longitudinal vibration in transducer in this can obtain a high offrustum a cone. of The vibration transducer this structure canstructure obtain a high transmitting transmitting voltage response. When the parameters of the transducer are optimally designed, the voltage response. When the parameters of the transducer are optimally designed, the longitudinal longitudinal resonant frequency is close to the cavity resonant frequency; so ofthe of of the resonant frequency is close to the cavity resonant frequency; so the resonance theresonance fluid cavity fluid cavity of the free‐flooded aluminum ring couples with the longitudinal vibration transducer, the free-flooded aluminum ring couples with the longitudinal vibration transducer, and a higher and a higher transmitting voltage response can be obtained. transmitting voltage response can be obtained.
Figure 1. The structure of the transducer.
Figure 1. The structure of the transducer.
The resonant frequency in the fluid cavity of the aluminum ring is given by Equation (1) as shown in Reference [12]: frequency in the fluid cavity of the aluminum ring is given by Equation (1) as The resonant q −1/2 rH shown in Reference [12]: ρ 0 c 2 f1 = 1+ (1) 1/2 2πr ρt
rH ρ0 2 ring, ρ0 = 1000 kg/m3 is the density(1) In this formula, r = 59 mm is the radius cof the aluminum of f 1 water, ρ = 2700 kg/m3 is the density of 1aluminum, is the height of the aluminum ring, 2πr H =ρt110 mm t = 2 mm is the thickness of the aluminum ring, and c = 5200 m/s is the speed of sound in aluminum,
so that the calculated cavity resonant frequency is f1 = 4040 Hz. 3 The resonant frequency of longitudinal vibration given byring, Equation (2) as shown r 59 mm In this formula, is the radius of the is aluminum ρ0 1000 kg/m is in the Reference [12]: r density of water, ρ = 2700 kg/m³ is the density of aluminum, H 110 mm is the height of the 1 Km c 5200 m/s is the speed of (2) f2 = aluminum ring, t 2 mm is the thickness of the aluminum ring, and 2π Mm sound in aluminum, so that the calculated cavity resonant frequency is f1 4040 Hz .
Reference [12]:
f2 Sensors 2018, 18, 3128
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In the formula, km is the stiffness of the piezoelectric ceramic stack, and Mm is the dynamic mass. the of the longitudinal vibration transducer, longitudinal resonant InAccording the formula,to km is size the stiffness of the piezoelectric ceramic stack, andthe Mm is the dynamic mass. frequency of the transducer is 4156 Hz, which is close to the above cavity resonant frequency. According to the size of the longitudinal vibration transducer, the longitudinal resonant frequency of the transducer is 4156 Hz, which is close to the above cavity resonant frequency. 3. Finite Element Modeling and Principle of Operation of the Transducer 3. Finite Element Modeling and Principle of Operation of the Transducer Since the transducer is axisymmetric, and symmetric up and down, the 2‐D axisymmetric finite Since the transducer is axisymmetric, and symmetric up and down, the 2-D axisymmetric finite element model can be used to calculate the transmitting characteristics of the transducer. Only the element model can be used to calculate the transmitting characteristics of thesymmetric conditions transducer. Only the upper half of the transducer needs to be modeled, as shown in Figure 2. The upper half of the needs to be modeled, as shown Figure 2. Theceramic symmetric conditions were were applied to transducer improve the simulation efficiency. The inpiezoelectric stack consisted of applied to improve the simulation efficiency. The piezoelectric ceramic stack consisted of 24 pieces of 24 pieces of PZT4 ceramics. The thickness of each ceramic was 4 mm and the radius was 10 mm. The PZT4 ceramics. The thickness of each ceramic was 4 mm and the radius was 10 mm. The polarization polarization direction was the Y‐axis direction, which was the longitudinal direction. The adjacent direction was the Y-axis which was thedirection. longitudinal The adjacent two ceramics two ceramics had the direction, opposite polarization The direction. driving voltages were exerted on had the the opposite polarization direction. The driving voltages were exerted on the piezoelectric ceramics. piezoelectric ceramics. The head mass of the transducer was made of steel, the maximum radius was The head mass of the transducer was made of steel, the maximum radius was 38 mm, and the height 38 mm, and the height was 16 mm. The free‐flooded ring was made of aluminum, the inner radius of was 16 mm. The free-flooded ring was made of aluminum, the inner radius of the ring was 60 mm, the ring was 60 mm, the height was 100 mm, and the thickness was 8 mm. In the ANSYS software, the height was 100 mm, and the thickness was 8 mm. In the ANSYS software, the geometry of the the geometry of the transducer was drawn using the above size, and then meshed to obtain the finite transducer was drawn using the above size, andYoung’s then meshed to obtain finite element Inand the element model. In the model, the density, modulus and the Poisson’s ratio model. of steel model, the density, Young’s modulus and Poisson’s ratio of steel and aluminum materials, the density, aluminum materials, the density, dielectric constant, piezoelectric constant, and elastic constant of dielectric constant, piezoelectric constant, and elastic constant of piezoelectric ceramics, and the density piezoelectric ceramics, and the density and sound velocity of the fluid are needed. In addition, the and sound velocity of the fluid are needed. In addition, the piezoelectric ceramics were assigned piezoelectric ceramics were assigned by Plane13 element; the aluminum ring and steel head mass by Plane42; the water area by Fluid29; and the outermost water layer by the Fluid129 to simulate the by Plane13 element; the aluminum ring and steel head mass by Plane42; water area by Fluid29; nonreflecting boundary; which were all axisymmetric elements. The radius of the fluid area should and the outermost water layer by Fluid129 to simulate the nonreflecting boundary; which were all satisfy the far‐field condition and be large as possible a condition high precision of axisymmetric elements. The radius ofselected the fluidas area should satisfy to theachieve far-field and be calculation. The condition which should usually be satisfied is: selected as large as possible to achieve a high precision of calculation. The condition which should usually be satisfied is: D R> D +0.2λ (3) R > 2 + 0.2λ (3) 2 where distance from the center of the transducer to the outermost boundary of the fluid area, where RRis the is the distance from the center of the transducer to the outermost boundary of the fluid D is the maximum size of the transducer structure, and λ is theλsound wavelength. area, D is the maximum size of the transducer structure, and is the sound wavelength.
Figure 2. The finite element model of the transducer. Figure 2. The finite element model of the transducer.
The acoustic radiation characteristics of the transducer in water can be calculated by harmonic response analysis in ANSYS, based on the finite element model. The transmitting voltage response (TVR) of the transducer is calculated by: TVR = 20 × log(p(r) × r/pref )
(4)
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The acoustic radiation characteristics of the transducer in water can be calculated by harmonic response analysis in ANSYS, based on the finite element model. The transmitting voltage response (TVR) of the transducer is calculated by: Sensors 2018, 18, 3128
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TVR = 20 × log(p(r) × r/pref)
(4)
where p(r) is the far‐field pressure generated at r meter range by the transducer in water when the where p(r) is the far-field pressure generated at r meter range by the transducer in water when the driving voltage is 1 V, which can be collected in the finite element model directly, pref = 1 μPa is the driving voltage is 1 V, which can be collected in the finite element model directly, pref = 1 µPa is the reference pressure. reference pressure. 4. Finite Element Analysis and Experimental Verification of the Transducer 4. Finite Element Analysis and Experimental Verification of the Transducer The finite element model of the free‐flooded transducer based on fluid cavity structure is shown The finite element model of the free-flooded transducer based on fluid cavity structure is in Figure 2. The admittance simulation curve of the transducer is shown by the dotted line in Figure 3a, shown in Figure 2. The admittance simulation curve of the transducer is shown by the dotted and the transmitting voltage response curve of the transducer is shown by the dotted line in Figure 3b. line in Figure 3a, and the transmitting voltage response curve of the transducer is shown by the dotted The admittance and transmitting voltage response of the transducer were measured in the anechoic line in Figure 3b. The admittance and transmitting voltage response of the transducer were measured water tank, and the measured results are shown by the solid lines in Figure 3a,b, respectively. The in the anechoic water tank, and the measured results are shown by the solid lines in Figure 3a,b, resonant frequency of the frequency transducer 4650 Hz from admittance simulation results by the respectively. The resonant ofwas the transducer wasthe 4650 Hz from the admittance simulation finite element method. The method. maximum transmitting voltage response was 129.5 dB at 4650 results by the finite element The maximum transmitting voltage response was 129.5Hz dB by at simulation. The resonant frequency of the transducer was 4700 Hz from the experimental 4650 Hz by simulation. The resonant frequency of the transducer was 4700 Hz from the experimental admittance results. results. The maximum transmitting voltage response dB Hz by admittance The maximum transmitting voltage response was 130was dB at130 4700 Hzat by4700 experiment. experiment. The admittance and transmitting voltage response results of the transducer by finite The admittance and transmitting voltage response results of the transducer by finite element simulation element simulation were consistent with those by experiment. were consistent with those by experiment.
(a)
(b)
Figure 3.3. (a) (a) The The simulated simulated and and measured measured admittance admittance results results of of the the transducer. transducer. The The solid red and and Figure solid red blue line, line, respectively, respectively, represent represent the the measured measured conductance conductance and and susceptance. susceptance. The The dotted dotted red red and and blue blue line, respectively, represent the simulated conductance and susceptance. (b) The simulated and blue line, respectively, represent the simulated conductance and susceptance. (b) The simulated and measured voltage response of the The solid dotted are the measured measured transmitting transmitting voltage response of transducer. the transducer. The and solid and line dotted line are the and simulated results, respectively. measured and simulated results, respectively.
The experiments were carried out in an anechoic water tank. The experiment diagram is shown The experiments were carried out in an anechoic water tank. The experiment diagram is shown in Figure 4. The computer generated the signals we needed and sent them to the data acquisition in Figure 4. The computer generated the signals we needed and sent them to the data acquisition and and transmission device. Then, the data acquisition and transmission device converted the digital transmission device. Then, the data acquisition and transmission device converted the digital signal signal to an analog signal, andsignal the signal was outputted totransducer the transducer power amplifying. to an analog signal, and the was outputted to the after after power amplifying. The The transducer transmitted the signal as an acoustic wave. Then, the hydrophone received the transducer transmitted the signal as an acoustic wave. Then, the hydrophone received the acoustic acoustic signal and transformed it into an electrical The data acquisition and transmission signal and transformed it into an electrical signal. signal. The data acquisition and transmission device device converted the analog signal into a digital signal and stored it in the computer for later converted the analog signal into a digital signal and stored it in the computer for later data data processing. the transmitting processing. Thus, Thus, the transmitting voltage voltage response response and and radiation radiation directivity directivity could could be be calculated. calculated. The 205 dB, The hydrophone hydrophone we we used used was was BK8104 BK8104 with with aa sensitivity sensitivity of of −−205 dB, at at the the frequency frequency range range of of 10 Hz–10 kHz. The distance between the transducer and hydrophone was 8.3 m, which satisfied the 10 Hz–10 kHz. The distance between the transducer and hydrophone was 8.3 m, which satisfied the far-field condition. far‐field condition.
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Figure 4. The diagram of the experiment. Figure 4. The diagram of the experiment. Figure 4. The diagram of the experiment.
5. Optimization of Radiation Directivity of the Transducer 5. Optimization of Radiation Directivity of the Transducer 5. Optimization of Radiation Directivity of the Transducer In the modeling and simulation of the transducer, it was found that the size of the aluminum In the modeling and simulation of the transducer, it was found that the size of the aluminum In the modeling and simulation of the transducer, it was found that the size of the aluminum ring around the outside of the transducer could not only change the transmitting voltage response of ring around the outside of the transducer could not only change the transmitting voltage response ring around the outside of the transducer could not only change the transmitting voltage response of the transducer, but also adjust the radiation directivity of the transducer. Through appropriate of the transducer, but also adjust the radiation directivity of the transducer. Through appropriate the transducer, but also adjust the radiation directivity of the transducer. Through appropriate optimization of the size of the aluminum ring, the radiation directivity of the transducer could be optimization of the size of the aluminum ring, the radiation directivity of the transducer could optimization of the size of the aluminum ring, the radiation directivity of the transducer could be improved. Two kinds of size of the aluminum ring were designed and the performances were be improved. Two kinds of size of the aluminum ring were designed and the performances were improved. Two kinds of size of the aluminum ring were designed and the performances were compared. Figure 5 shows the size of the aluminum ring before and after optimization. The thickness compared. Figure 5 shows the size of the aluminum ring before and after optimization. The thickness compared. Figure 5 shows the size of the aluminum ring before and after optimization. The thickness of the aluminum ring was changed from 2 mm to 8 mm, the radius was changed from 59 mm to of the aluminum ring was changed from 2 mm to 8 mm, the radius was changed from 59 mm to 60 mm, of 60 mm, and the total height was changed from 110 mm to 100 mm after optimization. Figure 6 shows the aluminum ring was changed from 2 mm to 8 mm, the radius was changed from 59 mm to and the total height was changed from 110 mm to 100 mm after optimization. Figure 6 shows 60 mm, and the total height was changed from 110 mm to 100 mm after optimization. Figure 6 shows the simulated and measured results of the radiation directivity of the transducer before and after the simulated and measured results of the radiation directivity of the transducer before and after the simulated and measured results of the radiation directivity of the transducer before and after optimization, at the resonant frequency of 4700 Hz. The 0° and 90° direction were the longitudinal optimization, at the resonant frequency of 4700 Hz. The 0◦ and 90◦ direction were the longitudinal optimization, at the resonant frequency of 4700 Hz. The 0° and 90° direction were the longitudinal and lateral direction of the transducer, respectively. The radiation directivity results simulated by the and lateral direction of the transducer, respectively. The radiation directivity results simulated by the and lateral direction of the transducer, respectively. The radiation directivity results simulated by the finite element method were consistent with the experimental results. The directivity of the transducer finite element method were consistent with the experimental results. The directivity of the transducer finite element method were consistent with the experimental results. The directivity of the transducer was improved after structure optimization, the beam pattern in the 90° direction was broadened and was improved after structure optimization, the beam pattern in the 90◦ direction was broadened and was improved after structure optimization, the beam pattern in the 90° direction was broadened and the transmitting response was higher in that direction, which is considered more useful in practical the transmitting response was higher in that direction, which is considered more useful in practical the transmitting response was higher in that direction, which is considered more useful in practical application. It verified the correctness of using the finite element method to simulate radiation application. It verified the correctness of using the finite element method to simulate radiation application. It verified the correctness of using the finite element method to simulate radiation directivity and improving the directivity by structure optimization of the transducer. directivity and improving the directivity by structure optimization of the transducer. directivity and improving the directivity by structure optimization of the transducer.
(a) (a)
(b) (b)
Figure 5. (a) The size of the aluminum ring before optimization. (b) The size of the aluminum ring Figure 5. (a) The size of the aluminum ring before optimization. (b) The size of the aluminum ring after optimization. Figure 5. (a) The size of the aluminum ring before optimization. (b) The size of the aluminum ring after optimization. after optimization.
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(a)
(b)
Figure 6. The (a) The simulated measured results of radiation the radiation directivity before optimization. Figure 6. (a) simulated and and measured results of the directivity before optimization. (b) The simulated and measured results of the radiation directivity after optimization. The solid and (b) The simulated and measured results of the radiation directivity after optimization. The solid and dotted lines are the measured and simulated results, respectively. dotted lines are the measured and simulated results, respectively.
6. Conclusions 6. Conclusions In this paper, the finite element method was used to calculate the transmitting voltage response, In this paper, the finite element method was used to calculate the transmitting voltage response, admittance curve, radiation directivity of the free-flooded transducer based on fluid cavity admittance curve, and and radiation directivity of the free‐flooded transducer based on fluid cavity structure, which was suitable for application in the deep sea. The influence of the size of the free-flooded structure, which was suitable for application in the deep sea. The influence of the size of the aluminumaluminum ring on thering radiation directivity the transducer was also analyzed. prototype of the free‐flooded on the radiation ofdirectivity of the transducer was A also analyzed. transducer was designed and fabricated, and experimental measurements were carried out in an A prototype of the transducer was designed and fabricated, and experimental measurements were anechoic water tank. The theoretical calculation results were consistent experimental results. carried out in an anechoic water tank. The theoretical calculation results with were the consistent with the It was verified that the finite element model was correct and feasible for the calculation and analysis of experimental results. It was verified that the finite element model was correct and feasible for the the transducer. The free-flooded transducer based on fluid cavity structure in this had good calculation and analysis of the transducer. The free‐flooded transducer based on paper fluid cavity performance, radiation directivity was improved by the optimal design of the transducer. structure in this and paper had good performance, and radiation directivity was improved by the
optimal design of the transducer. Author Contributions: Data curation, G.C. and Y.W.; Funding acquisition, Z.H.; Investigation, Z.H., G.C., Y.W., K.Z., and W.T.; Writing—original draft, Z.H. and G.C.; Writing—review and editing, Z.H., Y.W., K.Z., and W.T. Author Contributions: Data curation, G.C. and Y.W.; Funding acquisition, Z.H.; Investigation, Z.H., G.C., Y.W., Funding: This work was supported by the National Natural Science Foundation of China (Grant No. 11574251), K.Z., and W.T.; Writing—original draft, Z.H. and G.C.; Writing—review and editing, Z.H., Y.W., K.Z., and W.T. the Fundamental Research Funds for the Central Universities (Grant No. 3102017jg02017), and the Seed Foundation of Innovation and Creation for Graduate Northwestern Polytechnical (Grant Funding: This work was supported by the National Students Natural in Science Foundation of China University (Grant No. No. ZZ2018005). 11574251), the Fundamental Research Funds for the Central Universities (Grant No. 3102017jg02017), and the Conflicts of Interest: The authors declare no conflict of interest. Seed Foundation of Innovation and Creation for Graduate Students in Northwestern Polytechnical University (Grant No. ZZ2018005).
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