The low frequency axisymmetric modal sound radiation efficiency of an elastically supported annular plate

This paper deals with the sound radiation efficiency of a vibrating, thin, elastically supported annular plate embedded into a flat rigid baffle. The free axisymmetric time harmonic vibrations have been considered for a single mode. It has been assumed that the influence of the air column above the plate on the plate's vibrations is negligible. First, the sound radiation efficiency has been formulated as an integral. Further, rigorous mathematical manipulations have been carried out based on the theory of summation of multiple expansion series containing the hypergeometric functions. As a result, the formulations have been expressed as some fast convergent expansion series containing only the Bessel and Struve functions of integer order and the spherical Bessel functions. The presented formulations of sound radiation efficiency of an elastically supported annular plate are useful for numerical calculations within the low frequency range what is important for practical reasons. The formulations are valid for axisymmetric boundary conditions and they enable changing the values of boundary stiffness constants. Consequently, the analysis of influence of the plate's edge attachment on the sound radiation efficiency has been performed. The limiting transitions have also been performed from formulations valid for the elastically supported annular plates to the formulations valid for annular plates with classical boundary conditions (clamped, simply supported and free) at one edge or at both edges.     

有流条件下环形管道中的声传播特性

本文从线性波动方程出发,根据界面处声压连续和质点位移连续的条件,导得有流条件下无限长环形吸声管道中声传播的特征方程,并且具体分析了管道衰减系数与气流速度、壁面特性、截面几何尺寸和声波频率等参量的相互关系。研究表明,管道衰减系数随着气流流速的增加,管壁吸声系数的减小、管道截面几何尺寸的增加而减小。同时,随着声波频率从低频到高频的变化,衰减系数从小到大,再从大到小地变化,存在一个最佳峰值。     

各向同性矩形薄板的大振幅振动及其辐射声功率计算

采用有限元和模态叠加理论分析了固支及简支各向同性矩形薄板在集中简谐力作用下的大振幅振动,得出了薄板表面的法向振速分布,并采用声辐射模态法计算了薄板的辐射声功率.首先采用有限元理论推导了基于yon Karman几何非线性应变-位移关系的薄板非线性有限元运动方程,然后通过有限元模态约简法(finite element mo...     

The transmission of sound through a cavity-backed finite plate

This paper is concerned with the influence of a finite cavity backing a finite panel on the transmission of sound through the panel and on the vibration of the panel. Such phenomena as negative transmission loss, combined panel and cavity resonance, coincidence and cavity resonance are readily identified from the final expressions. A graphical technique, first used in a one-dimensional study of this case, is shown to be applicable in the three dimensional case to predict frequencies of interest. The theoretical analysis is compared with experimental results and with the predictions of other workers.     

幂函数型环形聚能器径向振动的等效电路

基于机电类比原理和变厚度薄圆环的平面应力方程,推导了幂函数型环形聚能器径向振动的等效电路、共振频率方程和位移放大系数。讨论了第一、二阶径向共振频率及相应的位移放大系数随圆环半径比的变化关系。结果表明,幂函数型环形聚能器径向振动的等效电路是一种非互易二端口等效网络;一阶和二阶共振频率随圆环内外半径比的增大而增大;一阶径向共振模式下位移放大系数随圆环半径比的增大先降低后升高,二阶径向共振模式下位移放大系数随圆环半径比的增大而降低,但二阶时的位移放大系数整体大于一阶,因此二阶径向共振模式具有更好的径向振动性能。用COMSOL有限元软件对解析理论分析结果进行了验证,仿真模拟结果与解析理论符合良好。根据幂函数型环形聚能器的等效电路模型,进一步设计了一种压电环形换能器,计算了第一、二阶径向共振频率、反共振频率及有效机电耦合系数,通过与COMSOL有限元软件模拟结果对比,符合良好。本文研究结果为幂函数型环形聚能器及压电环形换能器的工程应用提供了简明设计理论,文中研究结论可作为一种径向超声切割刀在超声工程中获得重要应用。     

Transmission of structure-borne sound from a beam into an infinite plate

An analytical study of transmission of structure-borne sound from a semi-infinite beam into an infinite, isotropic plate is presented. The beam is assumed to carry a torsional, a quasi-longitudinal and bending wave and the transmission is obtained with the help of the admittances of the beam and the plate. The analysis is restricted to the case of low frequencies but is otherwise general; thus due regard is given not only to the bending wave of the plate but also to the other propagating waves and to the local reactions. An interesting result from the study is that a bending wave on the beam will transfer a substantial part of its power into quasi-longitudinal and transverse waves in the plate, especially if the plate is thin compared with the beam. This is thought to be a factor that is important and not so easily quantifiable in the analysis of a complex structure. The local reactions on the other hand are of small importance for the power transmission from a torsional and quasi-longitudinal wave on the beam but may be important for the transmission of a bending wave, especially if the Young's modulus of the beam is larger than that of the plate.     

求解水中加肋板声辐射特性的虚拟声源法*

发展一种利用虚拟声源离散声场的方法求解加肋板在水中的声振耦合问题。由波叠加原理和单元体积速度匹配的原则,根据离散的结构单元满足的动力方程和结构与介质的交界相容性条件,确定虚拟声源强度,计算结构的声辐射功率。本文以简支矩形加肋板为例,在不获得结构表面振速和声压的情况下,计算了结构在水中的声辐射功率,并与解析方法计算的结果进行了比较,表明了该方法具有较好的计算精度。     

Scattering of sound by an elastic plate with flow

An elastic plate, set in an infinite baffle and immersed in a fluid moving with a uniform subsonic velocity, is excited by an acoustic source. The scattered sound field is analyzed when fluid-plate coupling is large, and a solution is found by the use of matched asymptotic expansions. The far field is found to approximate to the solution obtained when the elastic plate is absent. At a plate resonance, however, the outer field must include eigensolutions with singularities at the plate edges, and close to the plate the dominant terms are travelling plate waves. These plate waves are found to have a wavelength independent of the frequency of the source. It is also shown that a plate resonance corresponds to a divergence instability of aerodynamic flutter theory and that the stability results found in this paper are in agreement with those obtained by using modal expansions. The limit as the Mach number goes to zero is found to be singular, suggesting an analysis of the model for small flow velocity. This calculation is performed and the results match smoothly to the respective solutions for a stationary fluid and for a large subsonic flow.     

Effects of an air-layer-subdivision technique on the sound transmission through a single plate

Many studies on the sound transmission through a single plate have been carried out theoretically and experimentally. The transmission-loss characteristics, in general, follow mass law. Therefore, increasing mass of a plate is a fundamental measure to improve the insulation performance. This method, however, has limitations and might not be a reasonable alternative in current standards. Furthermore, the transmission loss at the critical frequency of coincidence is deteriorated significantly even if the mass is rather large. In this paper, the effect of the air-layer-subdivision technique is studied in detail from the viewpoint of the sound transmission problem of a single plate. An analytical model of an infinite single plate with a subdivided layer is considered and the improvement of the transmission loss is estimated. The limitations of the technique are clarified with some parametric studies. In order to validate the predictions, an experiment was carried out. The transmission loss of a glass board with the air layer subdivided by acryl partitions was measured in the experiment. They were in good agreement with the theoretical ones near and above the coincidence.     

带有相位拓朴数的环形相位板调控高斯光束的梯度力

 用基于德拜近似条件的矢量衍射理论研究了带有相位拓朴数的环形相位板调控高斯光束的光梯度力分布,改变相位板环形区的相对半径或当相位板的相位以一定拓扑数呈现拓扑变化时,可以调节光学系统焦点区域的光梯度力分布,形成各种非常有规则的几何形状的光陷阱,如当拓朴数分别取3,4,5,6时,可形成三角形、四边形、五边形和六边形光陷阱。此种相位板可用来构建可调的光镊系统,且通过调节相位板的各区域半径和拓扑数可以得到所希望的光陷阱。     

带有相位拓朴数的环形相位板调控高斯光束的梯度力

用基于德拜近似条件的矢量衍射理论研究了带有相位拓朴数的环形相位板调控高斯光束的光梯度力分布,改变相位板环形区的相对半径或当相位板的相位以一定拓扑数呈现拓扑变化时,可以调节光学系统焦点区域的光梯度力分布,形成各种非常有规则的几何形状的光陷阱,如当拓朴数分别取3,4,5,6时,可形成三角形、四边形、五边形和六边形光陷阱。此种相位板可用来构建可调的光镊系统,且通过调节相位板的各区域半径和拓扑数可以得到所希望的光陷阱。     

Theoretical analysis of sound radiation of an elastically supported circular plate

This study focuses on the analysis of the active and reactive sound power of the axisymmetric modes of free vibrations of elastically supported circular plates embedded in a rigid baffle. Some linear and time-harmonic processes have been considered. It is assumed that the plate radiates some acoustic waves into a hemisphere filled with a lossless gaseous medium. The integral formulations for the active and reactive sound power have been derived and expressed in their Hankel representations. They have been used to derive some elementary formulations in the form of some high-frequency asymptotes valid for frequencies higher than the successive coincidence frequencies of the plate. Therefore, the discussion on some sample numerical results mostly covers the sound power radiated at those frequencies. The asymptotes are easy to express in a computer code and they do not need great processor capacity. They are therefore useful for engineering use.The main benefit of the analysis presented in this paper is that the sound power for all the possible boundary configurations of the boundary stiffnesses, i.e., classical clamped, guided, simply supported or completely free boundaries as well as all the intermediate situations, has been described using the same formulae. This is possible simply by changing the two values of stiffnesses associated with the boundary conditions, whose influence on the radiated sound power has been discussed. The solution of the problem of sound power radiated by a vibrating elastically supported circular plate presented herein is essentially more general than the solutions presented earlier for the classical boundary configurations, such as clamped, simply supported, guided or completely free circular plates.     

弯管对末端带弹性障板充液管路辐射声能量的影响

基于声固耦合有限元方法建立了末端带弹性障板的充液管路数值模型,重点分析了不同激励下弯管对管口辐射声能量的影响。结果表明:弯管引入的高阶周向模式耦合使结构振动和流体声传播都发生明显改变,以致系统辐射声能量及主要能量贡献源也发生转移,并随激励方式和频率而不同。对本文管路模型,平面波激励下弯管系统在低频的结构辐射声能量明显增加,在高频段呈流体声与结构声交替主导的特点。径向力激励下直管系统的总声能量几乎全部来自于弹性障板辐射结构声,而弯管的声固耦合使得管口流体声功率显著增加。在轴向力激励下弯管耦合使系统总辐射声功率显著下降的同时管出口的流体声功率反而增加。     

弯管对末端带弹性障板充液管路辐射声能量的影响

基于声固耦合有限元方法建立了末端带弹性障板的充液管路数值模型,重点分析了不同激励下弯管对管口辐射声能量的影响。结果表明:弯管引入的高阶周向模式耦合使结构振动和流体声传播都发生明显改变,以致系统辐射声能量及主要能量贡献源也发生转移,并随激励方式和频率而不同。对本文管路模型,平面波激励下弯管系统在低频的结构辐射声能量明显增加,在高频段呈流体声与结构声交替主导的特点。径向力激励下直管系统的总声能量几乎全部来自于弹性障板辐射结构声,而弯管的声固耦合使得管口流体声功率显著增加。在轴向力激励下弯管耦合使系统总辐射声功率显著下降的同时管出口的流体声功率反而增加。     

Measurement of an individual silver perch Bairdiella chrysoura sound pressure level in a field recording

Simultaneous audio and video were recorded of a silver perch Bairdiella chrysoura producing its characteristic drumming sound in the field. The background noise contribution to the total sound pressure level is estimated using sounds that occurred between the pulses of the silver perch sound. This background contribution is subtracted from the total sound to give an estimate of the sound pressure level of the individual fish. A silver perch source level in the range 128-135 dB (re: 1 microPa) is obtained using an estimate of the distance between the fish and the hydrophone. The maximum distance at which an individual silver perch could be detected depends on the background sound level as well as the propagation losses. Under the conditions recorded in this study, the maximum detection distance would be 1-7 m from the hydrophone.     

正交加筋板声透射的板梁理论模型研究

为了研究正交加筋板的声透射问题,基于经典薄板和梁振动理论,建立了正交加筋板声透射的板梁理论模型。首先通过分析加强筋的受迫弯曲和扭转运动,求得了平板和加强筋线接触之间的反力和反力矩,然后将其引入到平板振动控制方程中,得到了正交加筋板声振方程,最后采用空间谐波展开法求解该方程得到了传声损失的表达式;在此基础上,首先研究了无限大平板和单向加筋的隔声性能,通过与解析解及两种简化模型的计算结果作对比,验证了所建理论模型的有效性;并进一步研究了加筋形式对正交加筋板隔声性能的影响。结果表明:选择合适的加筋形式可以有效避开结构的隔声波谷。     

Influence of an unbounded elastic plate on the radiation of sound by a point source

A sound source is placed at a finite distance from an unbounded elastic place. The source and the plate are submerged in an unbounded fluid at rest. The source has harmonic time dependence. A linear theory is used to compute how much energy is radiated into the fluid and how much energy travels along the plate from the source to infinity.