方板阶梯辐射体辐射声场的计算及测试

研究了一种同相弯曲振动方板阶梯辐射体。以边长50 mm的方形平板为例,材料为钢,厚度为6mm。其第四阶本征振型的频率为19332 Hz,用同频率的纵振换能器激励其中心,会出现节线与边长成45°夹角的响应(本征振型中无)。为了获得辐射体辐射声场的高指向性,在四个板角与四条节线围成的等腰直角三角形区域加阶梯,可将平板辐射体改进成阶梯辐射体。计算得到阶梯辐射体的指向性比平板辐射体的指向性尖锐,与方板活塞辐射体的指向性相似。实验测试辐射体指向性与计算结果基本一致。进一步计算发现,方板阶梯辐射体与线性尺寸相同的矩形、圆盘阶梯辐射体比较,其频率低,指向性同样尖锐,可望应用于超声测距、料位测试中。      

The relationship between acoustic radiation modes and structural modes and its applications

Both acoustic radiation modes and structural modes play an important role in the field of structure-borne sound, however, little work has been done for inherent relations between these two kinds of modes. This paper is focused on the relationship between the radiation modes and structural modes and its physical mechanisms. First, a governing equation for relating the radiation mode and structural mode is given based on the characteristics of the modes. Then, using the symmetric or anti-symmetric properties of two kinds of modes, the corresponding relations are presented. And then, numerical examples are given to verify the theoretical investigations, and it has been shown that, for a simply supported rectangular panel vibrating at low frequencies, the first radiation mode is dominant corresponding to (odd, odd) structural modes; the following radiation modes are respectively dominant corresponding to (even, odd), (odd, even), and (even, even) structural modes. Finally, such relations are applied to active acoustic structural control and provide a direct help for the design of active control strategy and arrangement of the secondary forces.     

The effects of distributed masses on acoustic radiation behavior of plates

The acoustic radiation behavior of a plate with a distributed mass loading is studied. A set of in vacuo normal modes or fluid-loaded undamped normal modes are used for modal analysis of the acoustic radiation from a plate in air or in water. Modal radiation efficiency, modal volume displacement, modal input energy and sound power level are computed to show the effects of size and location of the mass loading on the acoustic radiation of the plate. It is observed that the acoustic radiation behavior of a mode in both cases will have relatively larger changes if the mass loading is placed on an antinode of the mode shape or the mass loading is more concentrated. The acoustic radiation behavior of a mode and the radiated power of the plate in water have less change than those in air with the same mass loading due to the added mass of the water, especially for the first few modes.     

STUDY ON THE RADIATION ACOUSTIC FIELD OF RECTANGULAR RADIATORS IN FLEXURAL VIBRATION

In this paper, the radiation acoustic field of a rectangular radiator in flexural vibration is studied. The radiator is a rectangular thin plate in flexural vibration with simply supported boundary conditions. Based on the theory of Rayleigh integral, the acoustic pressure distribution of the radiator in its far field is obtained analytically and the near acoustic field of the radiator is also computed numerically. In the near field, the three-dimensional acoustic pressure distribution is obtained. In the far field, the two- and three-dimensional acoustic pressure distribution patterns are calculated. The dependence of the radiation acoustic pressure of the radiator on the vibrational order of the plate in flexural vibration is analyzed. It is demonstrated that the radiation acoustic pressure along the central axis of the radiator is always zero in the near and far acoustic fields, and the radiation near acoustic field and the far acoustic field are both directional. This is different from the acoustic field generated by an oscillating piston. On the other hand, when the vibrational order is increased, the acoustic pressure distribution of the radiator becomes complex.     

利用声辐射模态对声场进行重构

声辐射模态是定义在振动表面上的一组互相独立的基函数,描绘了振动表面的多极子辐射模式。本文利用声辐射模态对平板辐射的声场进行重构，并同时就频率和模态数对误差的影响进行了分析。针对复杂振动表面幅射的声场，重构时需正则化处理。数值计算结果和对应的理论值达到很好的吻合。     

Radiation efficiency of submerged rectangular plates

The average radiation efficiency of point-excited submerged rectangular plates is investigated in two methods, deterministic analysis and statistical approach, respectively. In the deterministic analysis, the effect of mutual impedance by water loading on the velocity of the plate is illustrated analytically by using a modal summation method. The cross-modal contributions to the average radiation efficiency are averaged to zero by averaging over all possible excitation positions on the plate. In the statistical approach, by analyzing the engineering formulae of the average radiation efficiency in air, this paper modifies the formulae to be applicable in water. The numerical comparisons show that the modified formulae reflect the average level in the frequency region controlled by corner modes and are accurate enough in the region controlled by monopole and edge modes. On this basis, approximate expressions for predicting the average radiation efficiency of the submerged beam-stiffened rectangular plates are proposed. The main differences between air loading and water loading are considered. Firstly, as dry modes taken in analysis instead of real vibration modes in water, the vibration of the stiffened plate is not only determined by the first mode but by several modes simultaneously at low frequencies. Secondly, the “corner mode region” becomes inappropriate as the plate is stiffened. The proposed formulae are validated numerically in different size, thickness, and stiffener amount of the stiffened plate.     

On the growth rate of bending induced edge cracks in acoustically excited panels

Parts of an aircraft structure may be made to vibrate as a result of acoustic waves generated by various aircraft noise sources impinging on the structure. The stresses associated with this acoustically induced vibration may be sufficiently large to result in fatigue failure of portions of the structure. If acoustically induced fatigue cracks occur in the stiffened skin structures widely used in aircraft construction they may initiate in the skin panels near the stiffener attachment points. The initiation and subsequent propagation of these cracks at the panel edges is primarily due to the bending stresses arising from the out-of-plane vibration of the individual skin panels.The emphasis of the work described in this paper is on examining the growth rate of edge cracks in acoustically excited panels. A single panel with an edge crack is considered and this structural element is modelled as a flat plate clamped on three edges and part of the fourth. The crack is represented by the unclamped part of the fourth edge. Fracture mechanics principles are used to predict the crack growth rates associated with the first two modes of vibration of the edge cracked panel. The crack tip stress intensity factors associated with these panel modes are estimated by a technique based on finding the nominal bending stresses at the crack tips. The nominal bending stresses are in turn found from mode shapes determined by the Rayleigh Principle. The validity of the various assumptions is assessed by comparing the predicted crack growth rates with measured growth rates in panels representative of those used in aircraft construction.     

Investigation of acoustic waves of higher order propagating in plates of lithium niobate

This paper presents theoretical investigation of higher order acoustic plate waves propagating in single crystals of lithium niobate. The dependencies of wave velocity and electromechanical coupling coefficient of antisymmetric, symmetric, and shear horizontal modes on the parameter hf (h=plate thickness, f=operating frequency) are calculated as a function of propagation direction on X-, Y-, and Z-cut lithium niobate plates. It is found that several modes can provide values of K2 that are much greater than can be obtained with surface acoustic waves (SAWs). For example, K2 as high as 0.26 and 0.38 can be obtained from SH1 and A2 modes, respectively. This compares with a maximum value of K2=0.055 for SAWs. It is further shown that there are several crystal cut and propagation directions that can allow efficient excitation and detection of a single mode with minimal interference due to other modes.     

Acoustic characteristics of a rocket combustion chamber: Radial baffle effects

This paper describes methods used for determining the characteristic acoustic modes and frequencies of a liquid-propellant rocket-motor combustion chamber and effects of radial baffles on the chamber’s acoustic field. A multi-point sensing experimental setup, including stationary and moving sensors, was used to measure characteristic frequencies and mode shapes of a combustion chamber. A new technique based on the comparison of signal phase angles from stationary sensors to that of a moving sensor was used to map complex characteristic mode shapes of a combustor. A three-dimensional Helmholtz acoustic solver was also developed using an efficient finite volume approach for complex geometries to simulate the acoustic field inside a combustor. Using this approach the effects of the convergent section of the nozzle and the number of radial baffles on the chamber’s dominant acoustic modes with no mean flow were investigated. We have shown that the classical reduction of characteristic frequency of tangential modes caused by radial baffles is due to longitudinalization of tangential modes and is a function of the blade length and weakly dependent on the number of blades. Also, conjugate spinning modes are decoupled and do not spin in any baffled combustor, independent of the number of blades. On the other hand the converging nozzle section of a combustion chamber modifies pure longitudinal modes in the radial direction and pure tangential modes in the longitudinal direction. Existence of some mixed tangential-longitudinal modes in a combustor is dependent on the ratio of the nozzle throat diameter to the combustor head plate diameter.     

Nodal line optimization and its application to violin top plate design

In the literature, most problems of structural vibration have been formulated to adjust a specific natural frequency: for example, to maximize the first natural frequency. In musical instruments like a violin; however, mode shapes are equally important because they are related to sound quality in the way that natural frequencies are related to the octave. The shapes of nodal lines, which represent the natural mode shapes, are generally known to have a unique feature for good violins. Among the few studies on mode shape optimization, one typical study addresses the optimization of nodal point location for reducing vibration in a one-dimensional beam structure. However, nodal line optimization, which is required in violin plate design, has not yet been considered. In this paper, the central idea of controlling the shape of the nodal lines is proposed and then applied to violin top plate design. Finite element model for a violin top plate was constructed using shell elements. Then, optimization was performed to minimize the square sum of the displacement of selected nodes located along the target nodal lines by varying the thicknesses of the top plate. We conducted nodal line optimization for the second and the fifth modes together at the same time, and the results showed that the nodal lines obtained match well with the target nodal lines. The information on plate thickness distribution from nodal line optimization would be valuable for tailored trimming of a violin top plate for the given performances.     

The song of the singing rod

This paper discusses basic and advanced aspects of the sound radiated by the singing rod demonstration commonly used in physics courses to depict an example of longitudinal waves. Various methods of exciting these rods are discussed along with the issues associated with each method. Analysis of the sound radiated by various rods with small-signal and large-signal excitations is presented for four different rods. The small-signal sound radiation consists of a fundamental frequency and odd harmonics (each corresponding to a longitudinal mode) when the rod is held at its midpoint. Large-signal sound radiation is highly dependent on the rod's geometry. The large-signal sound can possess strong even harmonics and/or beating tones resulting from modal coupling of transverse bending modes and either subharmonic longitudinal modes or torsional modes. A detailed analysis of the sound radiation from a singing rod can provide excellent laboratory exercises or classroom demonstrations for advanced undergraduate or graduate level acoustics courses whose scope includes resonances of a bar.     

The local vibration modes due to impact on the edge of a viaduct

This paper describes the vibration responses of a cement viaduct model under impulsive force excitation. The frequencies and mode shapes of resonances can control magnitude of the structure-borne noise radiation. A steel hammer is used to excite the cement viaduct model at the centre and at the supporting edge position of the cross-section separately in order to acquire the vibration responses and mode shape data. From such data the global mode and local modes of the cement viaduct model are identified. It is shown that the edge of section supported by the web may have low impedance in the vertical direction. The results of analysis using a Finite Element Method confirmed the experimental findings of the cross-sectional modes of the cement viaduct model. The findings suggested that the vibrations of local modes are of two types: (1) Centre mode - the centre of top panel can move but the edge is fixed. (2) Edge (web) mode - the centre of panel is fixed but the edge (supported by web) can move.     

A two-dimensional analysis of surface acoustic waves in finite elastic plates with eigensolutions

It is generally known that surface acoustic waves, or Rayleigh waves, have different mode shapes in infinite plates. To be precise, there are both exponentially decaying and growing components in plates appearing in pairs, representing symmetric and antisymmentric modes in a plate. As the plate thickness increases, the combined modes will approach the Rayleigh mode in a semi-infinite solid, exhibiting surface acoustic wave deformation and velocity. In this study, the two-dimensional theory for surface acoustic waves in finite plates is extended to include the exponentially growing modes in the expansion function. With these extra equations, we study the surface acoustic waves in a plate with different thickness to examine the coupling of the exponentially decaying and growing modes. It is found that for small thickness, the two groups of waves are strongly coupled, showing the significance of including the effect of thickness in analysis. As the thickness increases to certain values, such as more than five wavelengths, the exponentially decaying modes alone will be able to predict vibrations of surface acoustic wave modes accurately, thus simplifying the equations and solutions significantly. Supported by Qianjiang River Fund established by Zhejiang Provincial Government and Ningbo University and administered by Ningbo University and the National Natural Science Foundation of China (Grant No. 10572065)     

板结构的声辐射模态分析及其高分辨率法向振动速度重建

提出了一种基于声辐射模态的速度基向量构建方法,该速度基向量不受网格划分的影响,可用于高分辨率的板结构法向振动速度重建。首先对板表面稀疏网格的声辐射模态进行计算,再以声辐射模态和模态系数构建板法向振动速度分布的基向量,然后由声场测量声压求解基向量系数,最后由该系数和加密网格的速度基向量重建高分辨率的板法向振动速度分布。以简支板声源进行仿真计算,当测量声压信噪比为30 dB时,低频的法向振动速度重建误差最低可达3.7%;以固支板声源在消声室中进行实验验证,131.5 Hz振动频率下的重建误差低于7%。该方法实现了只需要少量声压测量点即可精确重建板声源更高分辨率的法向振动速度分布。      

基于声辐射模态的有源结构声传入及其辐射控制

从辐射模态的概念和角度研究利用结构误差传感方法对弹性封闭空间结构声辐射进行传感和有源控制。首先分析了辐射模态的数学和物理意义并揭示了辐射模态与声腔模态之间的内在耦合关系。通过声辐射模态建立了弹性封闭空间结构声辐射传感和有源控制模型,并提出了通过传感器阵列测量结构表面有限点的振速分布和设计特定的辐射模态空间滤波器来获得控制所需的误差信号。在此基础上对封闭空间结构声辐射有源控制和误差传感策略进行了深入的理论和数值仿真分析,重点讨论了传感器的数量和布放对辐射模态传感及其有源控制效果的影响。结果表明:辐射模态与声腔模态的耦合具有严格的选择性,各阶辐射模态的形状和与相耦合的主导声模态在耦合面上的形状非常相似;利用结构传感技术传感封闭空间的辐射模态时测点不足或空间采样不足将可能产生较严重的模态泄漏问题,使得不希望的结构模态泄露进所测的辐射模态当中来。在低频范围内,一般只需传感并最小化前三阶有效辐射模态声势能,在更低频和空间声模态频率附近,只需最小化前一阶最有效辐射模态声势能,便能和总声势能最小化策略控制效果基本一样。      

Reduction of sound radiation by using force radiation modes

The location of a vibration source within a machine is sometimes found to have a significant effect upon its radiated acoustic power. It is known that a simple reduction of vibration cannot always reduce the radiated acoustic power, so that treatments based on analysis of a structure’s vibration modes are not always effective. At the same time, radiation mode analysis is known to be a powerful tool for interpreting sound radiation since those modes are independent of a structure’s surface vibration. However, knowledge of the radiation modes alone cannot be used directly to understand the relationship between vibration source location and acoustic power radiation. In this paper, it is shown that the radiation mode concept can be extended to understand the relationship between acoustic power and driving force distribution by considering the product of the structure’s mobility matrix and the radiation modes: the resulting functions are here defined to be force radiation modes (f_rad-modes). An example is presented in which the acoustic power radiated by a simply-supported, baffled beam is reduced by using guidance provided by the structure’s force radiation modes. The results demonstrate that the force radiation modes can be used to guide the reduction of radiated acoustic power by changing the driving force location without the need to perform additional calculations or experiments.     

Parametric plate-bridge dynamic filter model of violin radiativity

A hybrid, deterministic-statistical, parametric "dynamic filter" model of the violin's radiativity profile [characterized by an averaged-over-sphere, mean-square radiativity (R(ω)(2))] is developed based on the premise that acoustic radiation depends on (1) how strongly it vibrates [characterized by the averaged-over-corpus, mean-square mobility (Y(ω)(2))] and (2) how effectively these vibrations are turned into sound, characterized by the radiation efficiency, which is proportional to (R(ω)(2))/(Y(ω)(2)). Two plate mode frequencies were used to compute 1st corpus bending mode frequencies using empirical trend lines; these corpus bending modes in turn drive cavity volume flows to excite the two lowest cavity modes A0 and A1. All widely-separated, strongly-radiating corpus and cavity modes in the low frequency deterministic region are then parameterized in a dual-Helmholtz resonator model. Mid-high frequency statistical regions are parameterized with the aid of a distributed-excitation statistical mobility function (no bridge) to help extract bridge filter effects associated with (a) bridge rocking mode frequency changes and (b) bridge-corpus interactions from 14-violin-average, excited-via-bridge (Y(ω)(2)) and (R(ω)(2)). Deterministic-statistical regions are rejoined at ~630 Hz in a mobility-radiativity "trough" where all violin quality classes had a common radiativity. Simulations indicate that typical plate tuning has a significantly weaker effect on radiativity profile trends than bridge tuning.     

Effect of acoustic field parameters on arc acoustic binding during ultrasonic wave-assisted arc welding

As a newly developed arc welding method, power ultrasound has been successfully introduced into arc and weld pool during ultrasonic wave-assisted arc welding process. The advanced process for molten metals can be realized by utilizing additional ultrasonic field. Under the action of the acoustic wave, the plasma arc as weld heat source is regulated and its characteristics make an obvious change. Compared with the conventional arc, the ultrasonic wave-assisted arc plasma is bound significantly and becomes brighter. To reveal the dependence of the acoustic binding force on acoustic field parameters, a two-dimensional acoustic field model for ultrasonic wave-assisted arc welding device is established. The influences of the radiator height, the central pore radius, the radiator radius, and curvature radius or depth of concave radiator surface are discussed using the boundary element method. Then the authors analyze the resonant mode by this relationship curve between acoustic radiation power and radiator height. Furthermore, the best acoustic binding ability is obtained by optimizing the geometric parameters of acoustic radiator. In addition, three concave radiator surfaces including spherical cap surface, paraboloid of revolution, and rotating single curved surface are investigated systematically. Finally, both the calculation and experiment suggest that, to obtain the best acoustic binding ability, the ultrasonic wave-assisted arc welding setup should be operated under the first resonant mode using a radiator with a spherical cap surface, a small central pore, a large section radius and an appropriate curvature radius.     

Theory and calculation for acoustic radiation mode of weak coupled enclosure

Active structural acoustic control(ASAC)is an efficient method in acoustic radiation control of coupled enclosure.In the past research of ASAC,the concept of "acoustic radiation mode(ARM)of coupled enclosure"was proposed,which was a set of basis functions of structural mode amplitude.However,there was an incompatibility with the ARM definition in free space radiation case which was a set of basic functions of normal velocity or pressure on the vibrating surface.Also,there was severe inconvenience for application as structural modes were required while accurate and useful structural modes were difficult to be extracted in practice.To overcome these problems,by analogy to ARM theory of free space,the acoustic potential energy was expressed in quadratic form of normal velocity on coupling surface and ARM of coupled enclosure was redefined.Furthermore,theoretic derivation showed that ARM of coupled enclosure could be replaced simply by corresponding acoustic mode projection of enclosure when the coupling surface was discretized into equal size elements.Therefore,the ARM theory of coupled enclosure which was consistent with that of free space and convenient for application was formed.Finally,numerical calculation was performed and the results proved that the presented theory was very efficient in ARM calculation of coupled enclosure and ASAC.     

Acoustic radiation force on a rigid cylinder near rigid corner boundaries exerted by a Gaussian beam field

Acoustic manipulation is one of the well-known technologies of particle control and a top research in acoustic field. Calculation of acoustic radiation force on a particle nearby boundaries is one of the critical tasks, as it approximates realistic applications. Nevertheless, it is quite difficult to solve the problem by theoretical method when the boundary conditions are intricate. In this study, we present a finite element method numerical model for the acoustic radiation force exerting on a rigid cylindrical particle immersed in fluid near a rigid corner. The effects of the boundaries on acoustic radiation force of a rigid cylinder are analyzed with particular emphasis on the non-dimensional frequency and the distance from the center of cylinder to each boundary. The results reveal that these parameters play important roles in acoustic manipulation for particle-nearby complicated rigid boundaries. This study verifies the feasibility of numerical analysis on the issue of acoustic radiation force calculation close to complex boundaries, which may provide a new idea on analyzing the acoustic particle manipulation in confined space.