Investigation of effects of viscoelastic boundary supports on transient sound radiated from a rectangular plate by modal strain energy method

This work considers analysis of transient sound radiation from an impact-excited rectangular plate with viscoelastic boundary supports based on the Modal Strain Energy (MSE) method. Vibration of the plate is approximated by double infinite series in the spatial coordinates. Each term of the series is constructed with vibration modes of beams having the same boundary conditions as the considered plate, multiplied by a time dependent function. Modal loss factor of each mode is obtained by the MSE method. The sound pressure for impact excitations is obtained in the time and frequency domain by numerical integration of the Rayleigh integral. Then effects of width of the viscoclastic boundary supports on the vibration response and the radiated sound pressure are investigated. It is shown that there is an optimum width of the support.     

声腔-弹性板结构在不同激励下声辐射特性研究

以声腔-弹性板声振耦合模型为研究对象,对比分析该模型在点力激励和点声源激励下,激励位置、声腔厚度以及弹性边界等对弹性板声辐射功率、表面振速和腔内声压的影响及两种情况下的区别。弹性板的振动位移函数通过谱几何方法得到,并采用Hamliton原理,充分考虑了板的振动与板两侧声场之间的耦合。利用Rayleigh积分,可计算出弹性板的声辐射特性参数。结果表明,在简支约束情况时,点力和点声源两种激励下,激励位置、声腔厚度和弹性边界对板的声辐射功率、表面振速和腔内声压有不同的变化。在薄声腔时,点力激励下,声腔个别模态对板有明显影响。点声源激励下,模型耦合作用明显,弹性板的声辐射功率、表面振速和腔内声压主要受到耦合模态的影响,且点声源的耦合作用明显强于点力作用。相较于扭转刚度,直线刚度对声辐射的影响更大。     

Effect of Wheel Load on Wheel Vibration and Sound Radiation

The current researches of wheel vibration and sound radiation mainly focus on the low noise damped wheel. Compared with the traditional research, the relationship between the sound and wheel/rail contact is difficulty and worth studying. However, there are few studies on the effect of wheel load on wheel vibration and sound radiation. In this paper, laboratory test carried out in a semi-anechoic room investigates the effect of wheel load on wheel natural frequencies, damping ratios, wheel vibration and its sound radiation. The laboratory test results show that the vibration of the wheel and total sound radiation decrease significantly with the increase of the wheel load from 0 t to 1 t. The sound energy level of the wheel decreases by 3.7 d B. When the wheel load exceeds 1 t, the attenuation trend of the vibration and sound radiation of the wheel becomes slow. And the increase of the wheel load causes the growth of the wheel natural frequencies and the mode damping ratios. Based on the finite element method(FEM) and boundary element method(BEM), a rolling noise prediction model is developed to calculate the influence of wheel load on the wheel vibration and sound radiation. In the calculation, the used wheel/rail excitation is the measured wheel/rail roughness. The calculated results show that the sound power level of the wheel decreases by about 0.4 dB when the wheel load increases by 0.5 t. The sound radiation of the wheel decreases slowly with wheel load increase, and this conclusion is verified by the field test. This research systematically studies the effect of wheel load on wheel vibration and sound radiation, gives the relationship between the sound and wheel/rail contact and analyzes the reasons, therefore, it provides a reference for further research.     

Nonlinear transient response analysis for double walls with a porous material supported by nonlinear springs using FEM and MSKE method

In this paper, we newly propose a fast computation method for the nonlinear transient responses including coupling between nonlinear springs and sound proof structures having porous materials using FEM. In this method, we extend our numerical method named as Modal Strain and Kinetic Method (i.e. MSKE method proposed previously by Yamaguchi who is one of the authors) from linear damping analysis to nonlinear dynamic analysis. We assume that the restoring force of the spring has cubic nonlinearity and linear hysteresis damping. To calculate damping properties for soundproof structures including elastic body, viscoelastic body and porous body, displacement vectors as common unknown variable are solved under coupled condition. The damped sound fields in the porous materials are defined by complex effective density and complex bulk modulus. The discrete equations in physical coordinate for this system are transformed into nonlinear ordinary coupled differential equations using normal coordinates corresponding to linear natural modes. Further, using MSKE method, modal damping can be derived approximately under coupled conditions between hysteresis damping of viscoelastic materials, damping of the springs and damping due to flow resistance in porous materials. The modal damping is used for the nonlinear differential equation to compute nonlinear transient responses.Moreover, using the proposed method, we demonstrate new vibration phenomena including nonlinear coupling between nonlinear springs and soundproof structures by use of a simplified model. As a typical numerical example of the soundproof structure, we adopt double walls with a porous material. The double walls are supported by nonlinear concentrated springs. We clarify influences of amplitude of the impact force on nonlinear transient responses. We focused on the vibration modes, which magnify the amplitudes of the double walls. In these modes, the internal air of the porous material played a role of a pneumatic spring. Under a very large impact force as a severe condition, there exist the complicated nonlinear couplings between these modes and the super harmonic components of the rigid modes of the whole structure with large deformations in the nonlinear springs.     

Sound radiation from strip plates with longitudinal stiffeners using waveguide finite and boundary element methods

In this study, the vibration characteristics and sound radiation of strip plates with finite width and infinite length are investigated numerically in order to analyze the vibration and sound radiation of structures consisting of many stiffened and double-layered plates. The waveguide finite element approach, which is effective for waveguide structures, is applied as a numerical scheme. The sound power and radiation efficiencies for an unstiffened plate are calculated numerically via coupling boundary elements to the WFEs. Longitudinal stiffeners and additional upper plates are included in the plate model to investigate the effect of stiffeners and an upper plate on sound power and radiation efficiency. In this study, it is found that the stiffeners contribute differently to plate vibration and sound radiation, and that the radiation efficiencies of the stiffened and double plates are larger than those of the unstiffened plate due to the presence of the stiffeners.     

基于声辐射模态的振动体积速度测量

在低频时,控制振动结构体积速度可以有效控制总声功率.体积速度与第一阶声辐射模态伴随系数近似成正比.通过在振动平板上测量少数点振动速度分布,求解得振动结构第一阶声辐射模态伴随系数近似值,从而获得体积速度,这就形成了一种基于声辐射模态的速度误差传感策略.增加测量点数,并不影响控制器的输入,控制系统实时性能够得到保证,重要的是这种误差传感策略适用任意边界条件的振动结构.以工程常见的四边位移为0的振动板为例,数值计算和实验结果分析表明,利用这种误差传感策略获取体积速度是可行的.     

NUMERICAL SIMULATION OF SOUND RADIATION ON GEARBOX'S HOUSING

The fluid-structure coupling finite element model and the boundary element model of a complex gearbox＇s housing are built based on the theory of fluid-structure coupling finite element method and boundary element method. At the same time, the exciting forces of the housing are analyzed and applied to the finite element models. Firstly, vibration of the housing is calculated by the fluid-structure coupling finite element model; secondly, the calculated result is verified by the experiment; finally, sound radiation of the housing is calculated by the boundary element. According to the calculated results, the housing adds some ribs not only to increase the strength, but also to reduce the sound radiation of the housing. At last, the sound radiation of the modified housing is calculated, which shows that the sound radiation of the modified housing with ribs is lower.     

Dynamic Behaviors of Axially Moving Viscoelastic Plate with Varying Thicknessn

Structural components of varying thickness draw increasing attention these days due to economy and light-weight considerations. In view of the absence of research in vibration analysis of viscoelastic plate with varying thickness, this study devotes to investigate the dynamic behaviors of axially moving viscoelastic plate with varying thickness. Based on the thin plate theory and the two-dimensional viscoelastic differential constitutive relation, the differential equation of motion of the axially moving viscoelastic rectangular plate is derived, the plate constituted by Kelvin-Voigt model has linearly varying thickness in the y-direction. The dimensionless complex frequencies of axially moving viscoelastic plate with four edges simply supported are calculated by the differential quadrature method, curves of real parts and imaginary parts of the first three-order dimensionless complex frequencies versus dimensionless moving speed are obtained, the effects of the aspect ratio, thickness ratio, the dimensionless moving speed and delay time on the dynamic behaviors of the axially moving viscoelastic rectangular plate with varying thickness are analyzed. When other parameters keep constant, with the decrease of thickness ratio, the real parts of the first three-order natural frequencies decrease, and the critical divergence speeds of various modes decrease too, moreover, whether the delay time is large or small, the frequencies are all complex numbers.     

考虑边界条件的弹性长方体封闭结构腔辐射声场分析

在弹性板边界施加假想的弹簧系统模拟板的不同边界条件,利用汉密尔顿函数和瑞利-李兹方法,建立由2块四边弹性支承的弹性板及4块刚性板构成的封闭矩形腔外的辐射声场模型,推导腔体外辐射声场的解析解.该模型考虑两弹性板之间以及弹性板与腔体内声场之间的耦合.算例表明,低频段时两弹性板之间为弱耦合,辐射声场主要由受到外激励的结构所决定;支承板的线弹簧的刚度变化对辐射声场的影响较旋转弹簧大.同时,运用有限元法计算腔体内的声模态和弹性板的振动模态及其耦合系数,结合边界元法计算出腔体外的声压响应,并将此数值仿真结果与前面导出的解析结果进行比较,理论推导的正确性得到验证.     

铺设角度对层合板结构声功率的影响分析*

针对层合板结构铺设角度对前二阶声辐射模态幅值和辐射声功率的影响进行分析。利用分层理论结合有限元模型求解层合板的铺设角度与振动速度信息之间关系。通过声辐射模态理论,以某12层层合板结构为例,研究固定边界条件下的层合板辐射模态数、对称铺设角度、单向铺设角度以及激励力位置对声辐射模态幅值和辐射总声功率的影响。计算结果表明,在相同角度下,对称铺设层合板结构最大声功率值要小于单向角度铺设层合板结构最大声功率值;另外在低频时,对层合板结构辐射声功率起主要贡献的是前两阶辐射模态。并以某16层零度铺设的固定边界条件下的层合板结构为例,对复合材料层合板结构的声辐射模态幅值及声功率进行试验分析。     

TRANSVERSE VIBRATION CHARACTERISTICS OF VISCOELASTIC RECTANGULAR PLATE WITH CRACK

Based on the two-dimensional viscoelastic differential constitutive relation and the thin plate theory, the differential equations of motion of the viscoelastic plate with an all-over part-through crack are established and the expression of additional rotation induced by the crack is derived. The complex eigenvalue equations of the viscoelastic plate with crack are derived by the differential quadrature method, and the 8method is used at the crack continuity conditions. Dimensionless complex frequencies of a crack viscoelastic plate with four edges simply supported, two opposite edges simply supported and other two edges clamped are calculated. The effects of the crack parameter, the aspect ratio and dimensionless delay time of the material on the transverse vibration of the viscoelastic plate are analyzed.     

Influence of support viscoelastic properties on the structural wave propagation

The dissipation of the structural vibration energy at viscoelastic supports is an efficient method of reducing modal resonances and consequent noise and fatigue related problems. The support stiffness has significant impact on the modal characteristics. The dissipation capabilities of the viscoelastic support depend on its stiffness. Methods to optimally tune this support stiffness are proposed in this study. The characteristic mechanical impedance for structural vibration is obtained from wave propagation analysis and non-reflecting boundary conditions. The wave propagation is analyzed near the supports installed at edges, middle of a structure, and for the tuned vibration absorber. The dependence of the optimal stiffness on the location and mass of the supports is identified. A simple analytical solution for optimal support stiffness for maximum dissipation of propagating vibration energy at supports is presented.     

结构阻尼的声衰减时间测量方法

针对结构阻尼的测量,通过分析平板的辐射声压,发现结构自由振动时的声压级的衰减率与平板的振动水平的衰减率相等.基于此提出了通过测量结构自由振动时的声衰减时间来计算结构损耗因子的测量方法,采用该方法及传统的测量方法测量得到的结构损耗因子在整个测试频率范围内基本相等.分析及实验结果表明,该方法正确可行,并且可实现结构阻尼的非接触测量.     

驾驶室结构振动及其声固耦合噪声响应分析

利用有限元分析软件ANSYS和声学分析软件SYSNO ISE对卡车驾驶室的振动与内部声场耦合做了数值计算分析研究。介绍了振动频响分析方法,动力学计算与声学边界元模型耦合的具体步骤。通过计算分析,分别研究了驾驶室结构的声固耦合模型与非耦合模型对室内声场的影响,从而找出在不同的壁板厚度条件下,声固耦合作用对室内噪声的影响,以及驾驶室内声场的变化规律。     

基于边界元理论的鼓风机组管路振动噪声控制研究

针对鼓风机组管路振动噪声问题,应用结构声辐射理论和结构振动测量数据分析振动声辐射强度。以实测振动信号为依据,根据对低频段计算精度较好的边界元理论,应用有限元软件和Sysnoise声学仿真软件建立了实际声场的边界元流体模型和有限元结构模型的耦合模型,得到了模拟声场的仿真结果,并与实测结果进行比较,确定了主要噪声能量来源于管路振动造成的结构振动。通过分析振动的来源以及振动传递的路径和传递特性,确定了隔振降噪的方法。依据理论分析结果,对实际现场采取了有效的隔振降噪方法,隔振后降噪效果明显。     

铁路客车车轮振动与声辐射特性分析

车轮是铁路客车上重要的声辐射部件。客车运行时,轮轨表面粗糙度使车轮产生振动及辐射噪声。利用有限元软件ABAQUS建立车轮的有限元模型,并计算0~10000 Hz内车轮的固有模态及振型。在车轮名义接触点施加单位力,采用模态叠加法,对车轮的频率响应函数进行分析。将车轮的频率响应作为边界条件,利用直接边界元法对其进行声辐射特性分析。     

弹性边界板结构拓扑优化声辐射

针对拓扑优化方法在减振降噪领域的应用以及板结构在实际应用中所处的环境,采用拓扑优化方法对不同弹性边界刚度的板结构进行拓扑优化分析,计算了不同边界刚度条件下板结构的声辐射情况。根据弹性边界板结构拓扑优化后的结构形式进行加强筋布置,对比于其他的加强筋布置形式进行板结构声学响应计算,得出了不同弹性边界刚度对于板结构拓扑优化结果的影响规律,以及不同板结构的边界刚度对于板结构声辐射情况的影响。板结构的声辐射响应计算结果验证了拓扑优化在减振降噪方面的应用价值。     

A novel prediction method of vibration and acoustic radiation for rectangular plate with particle dampers

Particle damping technology is widely used in mechanical and structural systems or civil engineering to reduce vibration and suppress noise as a result of its high efficiency, simplicity and easy implementation, low cost, and energy-saving characteristic without the need for any auxiliary power equipment. Research on particle damping theory has focused on the vibration response of the particle damping structure, but the acoustic radiation of the particle damping structure is rarely investigated. Therefore, a feasible modeling method to predict the vibration response and acoustic radiation of the particle damping structure is desirable to satisfy the actual requirements in industrial practice. In this paper, a novel simulation method based on multiphase flow theory of gas particle by COMSOL multiphysics is developed to study the vibration and acoustic radiation characteristics of a cantilever rectangular plate with Particle dampers (PDs). The frequency response functions and scattered far-field sound pressure level of the plate without and with PDs under forced vibration are predicted, and the predictions agree well with the experimental results. Results demonstrate that the added PDs have a significant effect on vibration damping and noise reduction for the primary structure. The presented work in this paper shows that the theoretical work is valid, which can provide important theoretical guidance for low-noise optimization design of particle damping structure. This model also has an important reference value for the noise control of this kind of structure.     

Vibration of circular Mindlin plates with concentric elastic ring supports

This paper studies the vibration behaviour of circular Mindlin plates with multiple concentric elastic ring supports. Utilizing the domain decomposition technique, a circular plate is divided into several annular segments and one core circular segment at the locations of the elastic ring supports. The governing differential equations and the solutions of these equations are presented for the annular and circular segments based on the Mindlin-plate theory. A homogenous equation system that governs the vibration of circular Mindlin plates with elastic ring supports is derived by imposing the essential and natural boundary and segment interface conditions. The first-known exact vibration frequencies for circular Mindlin plates with multiple concentric elastic ring supports are obtained and the modal shapes of displacement fields and stress resultants for several selected cases are presented. The influence of the elastic ring support stiffness, locations, plate boundary conditions and plate thickness ratios on the vibration behaviour of circular plates is discussed.     

基于局域共振的舰船浮筏低频减振方法

为控制动力机械激励下的舰船浮筏低频振动和噪声线谱,由变分原理建立了动力机械-平板-局域共振单元的耦合振动方程,采用模态叠加法导出了耦合振动方程的解,并给出了平板辐射声功率级的计算公式;设计了小尺寸轻质低频局域振子,分析了局域共振单元对动力机械激励下平板结构低频振动与辐射声功率线谱的控制效果。研究表明：在附加质量小于平板质量3%的要求下,局域共振单元可将低频振动线谱激励下平板结构表面平均振速级和辐射声功率级降低10%以上;当局域共振单元中包含多个固有频率不同的局域振子时,可以控制平板结构的多个低频振动与噪声线谱。