Broadband multimode baffled piezoelectric cylindrical shell transducers

Hollow piezoelectric cylindrical shell transducers may be made directional for underwater acoustic applications by the use of suitable acoustical baffles and the operational bandwidth may be extended by using multiple resonant modes. A theoretical and experimental investigation was performed for circumferentially baffled piezoelectric cylindrical shell transducers operating in the zero and one modes of extensional vibration. The frequency responses and directivity patterns were analyzed under various conditions of energizing separate halves of electrodes. It was found that the broadest frequency response with nearly constant beamwidth can be obtained when the two halves of the piezoelectric ring are electromechanically excited 90 deg out-of-phase. The experimental results obtained with a proof-of-concept transducer were in good agreement with the theoretical predictions.     

Acoustic radiation from a shell-encapsulated baffled cylindrical cap

An exact study of radiation of an acoustic field due to radial/axial vibrations of a baffled cylindrical piston, eccentrically positioned within a fluid-filled thin cylindrical elastic shell, into an external fluid medium is presented. This configuration, which is a realistic idealization of a liquid-filled cylindrical acoustic lens with a focal point inside the lens when used as a sound projector, is of practical importance with a multitude of possible applications in underwater acoustics and ocean engineering. The formulation utilizes the appropriate wave field expansions along with the translational addition theorems for cylindrical wave functions to develop a closed-form solution in the form of an infinite series. Numerical results reveal the key effects of excitation frequency, cap angle, radiator position (eccentricity), dynamics of the elastic shell, and cap surface velocity distribution on sound radiation.     

Cavitation bubble-driven cell and particle behavior in an ultrasound standing wave

The self- and mutual radiation impedances and the farfield directional response of rectangular pistons conformal to a rigid elliptic cylindrical baffle are formulated. The pistons are assumed to vibrate with uniform normal velocity and the solution for the acoustic pressure is expressed in terms of a modal series representation in Mathieu functions. The Mathieu functions are obtained using computer programs that have been recently developed to provide accurate values of the functions at high frequencies. Results for the normalized self- and mutual radiation resistance and reactance and the directional response of acoustic radiation are presented over a wide frequency range for different piston sizes and elliptic cylinder cross section shapes.     

Evaluation of mutual radiation impedances between circular pistons by impulse response and asymptotic methods

A general approach is presented to evaluate the mutual radiation impedance between circular pistons of arbitrary size and spacing in an infinite rigid planar baffle. The impedance is expressed as a Fourier transform of a generalized impulse response which is defined by an integral relationship. Although the integral must, in general, be numerically evaluated, several special cases of interest can readily be evaluated by using asymptotic techniques. Several asymptotic expressions for the mutual radiation impedance are developed and their limitations are noted. Numerical results are then presented for the generalized impulse response and mutual radiation impedance corresponding to pistons of equal size and arbitrary spacing. The time domain characteristics of the generalized impulse responses as a function of spacing are noted and related to the frequency characteristics of the mutual radiation impedances as a function of spacing. In addition, the accuracy of a simple closed form expression for the mutual radiation impedance is presented as a function of normalized frequency and spacing.     

Helmholtz水声换能器弹性壁液腔谐振频率研究

针对传统Helmholtz水声换能器设计中刚性壁假设的局限性,将Helmholtz腔体的弹性计入到液腔谐振频率计算中,实现低频弹性Helmholtz水声换能器液腔谐振频率精确设计.基于细长圆柱壳腔体的低频集中参数模型,导出了腔体弹性引入的附加声阻抗表达式,得到了弹性壁条件下Helmholtz水声换能器等效电路图,给出了考虑了末端修正的弹性壁Helmholtz共振腔液腔谐振频率计算公式.利用ANSYS软件建立了算例模型,仿真分析了不同材质、半径、长度时的Helmholtz共振腔液腔谐振频率.结果对比表明弹性理论值与仿真值符合得很好,相比起传统的刚性壁理论计算结果,本文的弹性壁理论得出的液腔谐振频率值有所降低,与真实情况更加接近.本文的结论可以为精确设计低频弹性Helmholtz水声换能器提供理论支持.     

Determination of acoustic impedances of multi matching layers for narrowband ultrasonic airborne transducers at frequencies <2.5 MHz - Application of a genetic algorithm

The effective ultrasonic energy radiation into the air of piezoelectric transducers requires using multilayer matching systems with accurately selected acoustic impedances and the thickness of particular layers. One major problem of ultrasonic transducers, radiating acoustic energy into air, is to find the proper acoustic impedances of one or more matching layers. This work aims at developing an original solution to the acoustic impedance mismatch between transducer and air. If the acoustic impedance defences between transducer and air be more, then finding best matching layer(s) is harder. Therefore we consider PZT (lead zirconate titanate piezo electric) transducer and air that has huge acoustic impedance deference. The vibration source energy (PZT), which is used to generate the incident wave, consumes a part of the mechanical energy and converts it to an electrical one in theoretical calculation. After calculating matching layers, we consider the energy source as layer to design a transducer. However, this part of the mechanical energy will be neglected during the mathematical work. This approximation is correct only if the transducer is open-circuit. Since the possibilities of choosing material with required acoustic impedance are limited (the counted values cannot always be realized and applied in practice) it is necessary to correct the differences between theoretical values and the possibilities of practical application of given acoustic impedances. Such a correction can be done by manipulating other parameters of matching layers (e.g. by changing their thickness). The efficiency of the energy transmission from the piezoceramic transducer through different layers with different thickness and different attenuation enabling a compensation of non-ideal real values by changing their thickness was computer analyzed (base on genetic algorithm). Firstly, three theoretical solutions were investigated. Namely, Chebyshev, Desilets and Souquet theories. However, the obtained acoustic impedances do not necessarily correspond to a nowadays available material. Consequently, the values of the acoustic impedances are switched to the nearest values in a large material database. The switched values of the acoustic impedances do not generally give efficient transmission coefficients. Therefore, we proposed, in a second step, the use of a genetic algorithm (GA) to select the best acoustic impedances for matching layers from the material database for a narrow band ultrasonic transducer that work at frequency below the 2.5 MHz by considering attenuation. However this bank is rich, the results get better. So the accuracy of the propose method increase by using a lot of materials with exact data for acoustic impedance and their attenuation, especially in high frequency. This yields highly more efficient transmission coefficient. In fact by using increasing number of layer we can increase our chance to find the best sets of materials with valuable both in acoustic impedance and low attenuation. Precisely, the transmission coefficient is almost equal to unity for the all studied cases. Finally the effect of thickness on transmission coefficient is investigated for different layers. The results showed that the transmission coefficient for air media is a function of thickness and sensitive to it even for small variation in thickness. In fact, the sensitivity increases when the differences of acoustic impedances to be high (difference between PZT and air).     

Sound radiation from point-excited structures: Comparison of plate and sphere

Acoustic radiation from a structure can be expressed in terms of “modal radiation” and “modal coefficients”. This paper investigates the contributions of these two modal properties to radiation excited by a point force. Sound radiation from two basic structures is considered: a baffled rectangular plate and a closed spherical shell. The plate behaviour is familiar, and governed by the relation between the natural frequency of a mode and its coincidence frequency. For a closed spherical shell, there are either zero or two “critical frequencies”, depending on the radius and thickness. When there are two the shell radiates well both above and below the two frequencies, and poorly in the frequency range between them.     

Estimation of interference of piezoelectric ceramic transducers in a hydroacoustic array

A method for experimental estimation of intrinsic and mutual impedances of transducers in a shipborne multielement hydroacoustic array is proposed and investigated. It is shown that consideration of the transducer interactions increases the radiated power and suppresses the lateral field.     

Energy trapping in power transmission through a circular cylindrical elastic shell by finite piezoelectric transducers

We study the transmission of electric energy through a circular cylindrical elastic shell by acoustic wave propagation and piezoelectric transducers. Our mechanics model consists of a circular cylindrical elastic shell with finite piezoelectric patches on both sides of the shell. A theoretical analysis using the equations of elasticity and piezoelectricity is performed. A trigonometric series solution is obtained. Output voltage and transmitted power are calculated. Confinement and localization of the vibration energy (energy trapping) is studied which can only be understood from analyzing finite transducers. It is shown that when thickness-twist mode is used the structure shows energy trapping with which the vibration can be confined to the transducer region. It is also shown that energy trapping is sensitive to the geometric and physical parameters of the structure.     

On the sound field of a shallow spherical shell in an infinite baffle

A method is presented for calculating the far field sound radiation from a shallow spherical shell in an acoustic medium. The shell has a concentrated ring mass boundary condition at its perimeter representing a loudspeaker voice coil and is excited by a concentrated ring force exerted by the end of the voice coil. A Green's function is developed for a shallow spherical shell, which is based upon Reissner's solution to the shell wave equation [Q. Appl. Math. 13, 279-290 (1955)]. The shell is then coupled to the surrounding acoustic medium using an eigenfunction expansion, with unknown coefficients, for its deflection. The resulting surface pressure distribution is solved using the King integral together with the free space Green's function in cylindrical coordinates. In order to eliminate the need for numerical integration, the radiation (coupling) integrals are solved analytically to yield fast converging expansions. Hence, a set of simultaneous equations is obtained which is solved for the coefficients of the eigenfunction expansion. These coefficients are finally used in formulas for the far field sound radiation.     

Acoustic radiation impedance of rectangular pistons on prolate spheroids

The self and mutual radiation impedances for rectangular piston(s) arbitrarily located on a rigid prolate spheroidal baffle are formulated. The pistons are assumed to vibrate with uniform normal velocity and the solution is expressed in terms of a modal series representation in spheroidal eigenfunctions. The prolate spheroidal wave functions are obtained using computer programs that have been recently developed to provide accurate values of the wave functions at high frequencies. Results for the normalized self and mutual radiation resistance and reactance are presented over a wide frequency range for different piston sizes and spheroid shapes.     

Scattering from an anisotropic cylindrical dielectric shell

The electromagnetic scattering from an anisotropic cylindrical dielectric shell is formulated by using the wave functions for anisotropic media and the boundary-value method. The cylindrical shell is assumed to be infinite in length, and it is illuminated by a plane wave or a cylindrical wave from a line source. The problem is two-dimensional and the solutions to both types of polarization (TE and TM) are presented. Numerical results for the effects of various geometrical and electrical parameters on the bistatic radar cross section are presented.     

The modeling of the radiation and response green's function of a fluid-loaded cylindrical shell with an external compliant layer

Scattering and radiation of acoustic waves from a fluid-loaded cylindrical shell with an external compliant layer are of interest. The compliant layer can be modeled by a normally reacting impedance layer, which has the advantage that complex compliant layer geometries, such as partial compliant layers, can be considered. A question may, however, arise as to the accuracy of this approach. A more rigorous approach is to model the elastic shell and compliant layer using a multilayer shell theory, which has the disadvantage that it cannot be extended to consider partial layers. In this paper scattering results from the normally reacting compliant layer model are compared to those from the multilayer shell model to show that the two approaches produce similar results, except for thickness resonances of the compliant layer. Having established the consistency between the two approaches, results for the far-field acoustic radiation as a function of frequency and radiation angle for a fluid-loaded shell with an external compliant layer excited by an internal ring force are obtained using the normally reacting impedance layer model. These results clearly show the reduction in the far field radiation due to the presence of the compliant layer.     

Influence of the thickness of multilayer matching systems on the transfer function of ultrasonic airborne transducer

The effective ultrasonic energy radiation into the air of piezoelectric transducers requires using multilayer matching systems with accurately selected acoustic impedances and the thickness of particular layers. This problem is of particular importance in the case of ultrasonic transducers working at a frequency above 1 MHz. Because the possibilities of choosing material with required acoustic impedance are limited (the counted values cannot always be realised and applied in practice) it is necessary to correct the differences between theoretical values and the possibilities of practical application of given acoustic impedances. Such a correction can be done by manipulating other parameters of matching layers (e.g. by changing their thickness). The efficiency of the energy transmission from the piezoceramic transducer through different layers with different thickness enabling a compensation of non-ideal real values by changing their thickness was computer analysed. The result of this analysis is the conclusion that from the technological point of view a layer with defined thickness is easier and faster to produce than elaboration of a new material with required acoustic parameter.     

Optimal locations and orientations of piezoelectric transducers on cylindrical shell based on gramians of contributed and undesired Rayleigh–Ritz modes using genetic algorithm

In this study, the active vibration control and configurational optimization of a cylindrical shell are analyzed by using piezoelectric transducers. The piezoelectric patches are attached to the surface of the cylindrical shell. The Rayleigh–Ritz method is used for deriving dynamic modeling of cylindrical shell and piezoelectric sensors and actuators based on the Donnel–Mushtari shell theory. The major goal of this study is to find the optimal locations and orientations of piezoelectric sensors and actuators on the cylindrical shell. The optimization procedure is designed based on desired controllability and observability of each contributed and undesired mode. Further, in order to limit spillover effects, the residual modes are taken into consideration. The optimization variables are the positions and orientations of piezoelectric patches. Genetic algorithm is utilized to evaluate the optimal configurations. In this article, for improving the maximum power and capacity of actuators for amplitude depreciation of negative velocity feedback strategy, we have proposed a new control strategy, called “Saturated Negative Velocity Feedback Rule (SNVF)”. The numerical results show that the optimization procedure is effective for vibration reduction, and specifically, by locating actuators and sensors in their optimal locations and orientations, the vibrations of cylindrical shell are suppressed more quickly.     

降低加肋双层圆柱壳辐射噪声线谱的结构声学设计

为降低双层圆柱壳辐射噪声线谱,从控制内壳振动响应和衰减壳间振动传递率进行结构声学设计。采用机械阻抗理论分析了环肋圆柱壳模态响应控制机理;由环肋振动方程推导分析了环肋径向机械阻抗特性;基于阻抗失配、波形转换原理提出一种阻抗加强环肋,分析了振动波阻抑特性;利用阻尼减振技术,综合考虑肋板的刚度、阻尼特性,设计了金属橡胶层叠肋板;结合数值计算实例,分析了设计双层壳模型的声辐射性能。结果表明:设计的双层加肋圆柱壳结构能有效降低辐射噪声线谱,在分析频段内辐射声压线谱平均降低约6.6 dB。研究结果对研制低噪声水下航行器具有良好的工程价值和应用前景。      

深水爆炸冲击波作用下圆柱壳动态响应影响因素的数值模拟研究

 运用通用有限元程序ABAQUS,对圆柱壳在深水爆炸冲击波作用下的动态响应进行了数值模拟,研究了圆柱壳所处深度、爆心方位和预应力对于圆柱壳动态响应的影响。研究结果表明：在同样的水下爆炸冲击波作用下,随着深度的增大,圆柱壳的毁伤逐渐加重,而且响应过程中的变形逐渐增大,低频响应阶段的速度曲线趋于平坦;爆距不变时,不同的爆心方位在不同深度上的毁伤效果存在一定差异;预应力的存在使圆柱壳的毁伤加重,并且预应力对圆柱壳动态响应的影响与爆心方位有关。研究结果对于潜体结构的生命力评估具有一定参考价值。     

An electro-acoustics impedance error criterion and its application to active noise control

Characteristics of radiation impedance and its inducing variation of electrical impedance for a controllable source have been investigated. An impedance-based error criterion has been proposed and its application to active noise control is demonstrated through a coil driven loudspeaker. A general formula of radiation impedance is derived for two control strategies, according to the criterion of total acoustic power output. The radiation impedances of some commonly used sound sources are calculated. We discuss in detail the relation between variation of the input electrical impedance and radiation impedance for the two control strategies. An AC-bridge circuit is designed to measure the weak variation of electrical impedance resulted from radiation impedance. The input electrical impedance of a loudspeaker was measured and the experimental result is consistent with that of theoretical analysis. An impedance-based error criterion is proposed since the AC-bridge relative output is unique for a certain control strategy. The implementation of this criterion applied to an active control system is analyzed by simulations. An analogue control system is set up and experiments are carried out in a semi-anechoic chamber to verify the new control approach.     

Improved precision in measurements of acoustic impedance spectra using resonance-free calibration loads and controlled error distribution

Resonances and/or singularities during measurement and calibration often limit the precision of acoustic impedance spectra. This paper reviews and compares several established techniques, and describes a technique that incorporates three features that considerably improve precision. The first feature is to minimize problems due to resonances by calibrating the instrument using up to three different acoustic reference impedances that do not themselves exhibit resonances. The second involves using multiple pressure transducers to reduce the effects of measurement singularities. The third involves iteratively tailoring the spectrum of the stimulus signal to control the distribution of errors across the particular measured impedance spectrum. Examples are given of the performance of the technique on simple cylindrical waveguides.     

Acoustic radiation analysis and experimental verification of a broadband dense plane array

The sound field distribution of a broadband array is calculated using the acoustics FEM and BEM.The FEM-BEM model is established for a nine-element plane array and its numerical method of calculating mutual radiation impedance among the transducers is given. The changing law of mutual radiation impedance influencing acoustics performances is analyzed. The directivity and beam width of the plane array are calculated at three resonance frequencies.A broadband dense plane array with nine elements is developed using triply resonant transducers.The input impedance and directivity of the plane array are measured in anechoic water tank.Results show that it is reasonable to design the array according to the half wavelengh of the first resonance frequency of the array element.The numerical solution agrees with the measuring results well,which indicates the FEM-BEM method is feasible to calculate sound field distribution and analyze mutual impedances.