On the acoustic radiation efficiency of local resonance based stop band materials

The application of materials with stop bands is emerging as a novel way of creating meta-materials with good vibrational behaviour. The acoustic radiation efficiency in these stop band zones is often not investigated. This paper formulates an uncoupled vibro-acoustic unit cell model of a plate with local resonant stop band behaviour, based on the addition of a grid of tuned resonators. The results are compared with a vibro-acoustic coupled model for a finite equivalent of the infinite structure. It is shown that the beneficial vibration reduction that is achieved in a stop band can be acoustically reduced or enhanced by the change in radiation efficiency of the structure. When care is taken in the design of the stop band, a stop band material with good vibro-acoustic behaviour can be achieved.     

Sound transmission through finite lightweight multilayered structures with thin air layers

The sound transmission loss (STL) of finite lightweight multilayered structures with thin air layers is studied in this paper. Two types of models are used to describe the vibro-acoustic behavior of these structures. Standard transfer matrix method assumes infinite layers and represents the plane wave propagation in the layers. A wave based model describes the direct sound transmission through a rectangular structure placed between two reverberant rooms. Full vibro-acoustic coupling between rooms, plates, and air cavities is taken into account. Comparison with double glazing measurements shows that this effect of vibro-acoustic coupling is important in lightweight double walls. For infinite structures, structural damping has no significant influence on STL below the coincidence frequency. In this frequency region, the non-resonant transmission or so-called mass-law behavior dominates sound transmission. Modal simulations suggest a large influence of structural damping on STL. This is confirmed by experiments with double fiberboard partitions and sandwich structures. The results show that for thin air layers, the damping induced by friction and viscous effects at the air gap surfaces can largely influence and improve the sound transmission characteristics.     

Finite element reduced order model for noise and vibration reduction of double sandwich panels using shunted piezoelectric patches

This work concerns the control of sound transmission through double laminated panels with viscoelastic core using semi-passive piezoelectric shunt technique. More specifically, the system consists of two laminated walls, each one composed of three layers and called sandwich panel with an air cavity in between. The external sandwich panel has a surface-mounted piezoelectric patches. The piezoelectric elements, connected with resonant shunt circuits, are used for the vibration damping of some specific resonance frequencies of the coupled system. Firstly, a finite element formulation of the fully coupled visco-electro-mechanical-acoustic system is presented. This formulation takes into account the frequency dependence of the viscoelastic material. A modal reduction approach is then proposed to solve the problem at a lower cost. In the proposed technique, the coupled system is solved by projecting the mechanical displacement unknown on a truncated basis composed by the first real short-circuit structural normal modes and the pressure unknown on a truncated basis composed by the first acoustic modes with rigid boundaries conditions. The few initial electrical unknowns are kept in the reduced system. A static correction is also introduced in order to take into account the effect of higher modes. Various results are presented in order to validate and illustrate the efficiency of the proposed finite element reduced order formulation.     

Vibro-acoustic response of an elliptical plate-cavity coupled system to external shock loads

A general fully coupled three-dimensional vibro-acoustic model is developed to investigate the forced non-stationary acousto-structural response of a thin elastic plate of elliptical planform which is backed by a reverberant, rigid, and finite (closed) elliptic cylindrical acoustic enclosure, while under the action of general external transverse loads of arbitrary temporal and spatial variations. The Laplace transform with respect to the time coordinate is invoked, and the classical method of separation of variables in elliptic coordinates is used to obtain the transformed solutions as a linear combination of even and odd modes in terms of products of radial and angular Mathieu functions. A linear system of coupled algebraic equations is ultimately obtained, which is truncated and then solved numerically by implementing Durbin’s numerical Laplace transform inversion scheme. Detailed numerical simulations are conducted for the temporal histories of plate center-point displacement and on-axis cavity acoustic pressure for air-coupled elliptic aluminum plates of selected aspect ratios when subjected to external loadings of practical interest (i.e., an impulsive point load, a uniformly distributed pulse load, and a blast load). Also, acoustic radiation into the backing enclosure is examined by using appropriate 2D images of the internal sound field for selected cavity depths and plate eccentricities. The presented results confirm that the acousto-elastic characteristics of the coupled plate-cavity system are significantly influenced by the plate aspect ratio, cavity depth and the transverse loading configuration. Validity of the work is established through the computations made by using a commercial finite element package.     

An improved model for the classical Huygens׳ experiment on synchronization of pendulum clocks

This paper introduces a new model for the classical Huygens? experiment on synchronization of two pendulum clocks hanging from a wooden coupling structure. The dynamics of the coupling—a beam with supporting structure—is modelled in detail using the finite element method. The pendula are considered as single dof systems with local nonlinearities—modelling the escapement. Consequently, the resulting coupled model consists of a finite set of nonlinear ordinary differential equations. Then, the existence of synchronous motion in the system is analytically investigated. Furthermore, this model is used in order to obtain numerical results illustrating the possible limit behaviour of the system. Besides in-phase and anti-phase synchronization, other kinds of limit behaviour appear, namely quenching, beating death, and modulating behaviour, phenomena, which ‘Huygens did not see’.     

传递矩阵法预报时空随机激励下任意薄壳腔体内部噪声

利用结构有限元结合声有限元及边界元方法,建立了任意薄壳腔体弹性壳板振动与内外声场的耦合模型,并计算了激励力与壳板振动和内部声场之间的传递矩阵;湍流边界层脉动压力具有时空随机面激励特性,引入整体形状函数矩阵,进一步推导弹性壳板广义节点力功率谱密度函数矩阵与随机面分布激励力功率谱密度函数的关系,再利用声振耦合传递矩阵,得到弹性壳板振动和内部声场功率谱密度函数与广义节点力功率谱密度函数矩阵的关系,形成随机分布激励下任意薄壳腔体结构振动及内部声场的计算方法。以典型的内外均有声介质且一面为弹性矩形板的矩形腔声振耦合模型为例,计算了弹性壳板振动和内部声场功率谱密度函数,并与解析方法进行了比较,两者基本吻合,偏差分别为1 dB和2 dB左右。传递矩阵法不受腔体结构及其内部区域形状的制约,具有良好的适用性。      

Vibro-acoustic analysis of a rectangular-like cavity with a tilted wall

In this paper, a fully coupled vibro-acoustic model is developed to characterize the structural and acoustic coupling of a flexible panel backed by a rectangular-like cavity with a slight geometrical distortion, which is introduced through a tilted wall. The combined integro-modal approach is used to handle the acoustic pressure inside the irregular-shaped cavity. Based on the model proposed, the distortion effect on the vibro-acoustic behavior of the coupled system is investigated using the averaged sound pressure level inside the enclosure and the averaged quadratic velocity of the vibrating plate. Simulations are conducted to examine the distortion effect on acoustic natural frequencies, acoustic pressures and structural responses. Effects of the wall inclination on coupling coefficients are also assessed, and an index is proposed to quantify the degree of variation of coupling strength.     

A hybrid finite element – statistical energy analysis approach to robust sound transmission modeling

When considering the sound transmission through a wall in between two rooms, in an important part of the audio frequency range, the local response of the rooms is highly sensitive to uncertainty in spatial variations in geometry, material properties and boundary conditions, which have a wave scattering effect, while the local response of the wall is rather insensitive to such uncertainty. For this mid-frequency range, a computationally efficient modeling strategy is adopted that accounts for this uncertainty. The partitioning wall is modeled deterministically, e.g. with finite elements. The rooms are modeled in a very efficient, nonparametric stochastic way, as in statistical energy analysis. All components are coupled by means of a rigorous power balance. This hybrid strategy is extended so that the mean and variance of the sound transmission loss can be computed as well as the transition frequency that loosely marks the boundary between low- and high-frequency behavior of a vibro-acoustic component. The method is first validated in a simulation study, and then applied for predicting the airborne sound insulation of a series of partition walls of increasing complexity: a thin plastic plate, a wall consisting of gypsum blocks, a thicker masonry wall and a double glazing. It is found that the uncertainty caused by random scattering is important except at very high frequencies, where the modal overlap of the rooms is very high. The results are compared with laboratory measurements, and both are found to agree within the prediction uncertainty in the considered frequency range.     

Dynamic stability of a sandwich plate with a constraining layer and electrorheological fluid core

The dynamic stability problems of a sandwich plate with a constraining layer and an electrorheological (ER) fluid core subjected to an axial dynamic force are investigated. The rectangular plate is covered in an ER fluid core and a constraining layer to improve the stability of the system. Effects of the natural frequencies, static buckling loads, and loss factors on the dynamic stability behavior of the sandwich plate are studied in the paper. Rheological property of an ER material, such as viscosity, plasticity, and elasticity may be changed when applying an electric field. The modal damper and the natural frequencies for the sandwich plate are calculated for various electric fields. When an electric field is applied, the damping of the system is more effective. In this study, finite element method and the harmonic balance method are used to calculate the instability regions of the sandwich plate. The ER fluid core is found to have a significant effect on the dynamic stability regions.     

On improving weakly coupled cavity models for vibro-acoustic predictions and design

The vibro-acoustic characteristics of a cavity based on its vibro-acoustic FE model at times do not correlate well with the corresponding measured vibro-acoustic characteristics. Structural dynamic modeling errors that are often associated with the structural domain of the cavity are the main reasons for this discrepancy. This paper addresses this issue and deals with the improvement of the vibro-acoustic FE models of weakly coupled cavities. This particular application, hitherto, has not been much addressed, though the improvement of purely structural dynamic systems has been researched a lot. An experimental example of a 3D rectangular-box cavity with a flexible plate is considered. The study demonstrates that the improvement of the vibro-acoustic FE models through FE model updating can be an effective approach to obtain more accurate vibro-acoustic predictions. The study further addresses the question whether these improved vibro-acoustic models are suitable for vibro-acoustic design. This is answered by analyzing the accuracy with which the improved vibro-acoustic FE model predicts the effects of the structural modifications. It is finally concluded that the predictions based on the unimproved vibro-acoustic models may not be reliable and can have significant error, while the improved vibro-acoustic models give an improvement in the predictive capability of the model and are also found suitable for vibro-acoustic design.     

An experimental validation of vibro-acoustic prediction by the use of simplified methods

Predicting the vibro-acoustic behaviour of a structure is usually done by using the well established finite element (FE) method and boundary element method. This paper presents a vibro-acoustic prediction case performed on a metal box using less accurate but simplified methods: sub-structuring for the calculation of the dynamic response of the structure, and a monopole distribution for the radiated noise calculation. Both are less accurate but faster methods than previous ones. An experimental validation was performed. It led to the conclusion that these methods give precise results and are sufficient for the pre-design of structures in the low frequency domain. However, this conclusion must be moderated by the fact that in spite of the simplicity of the structure, the FE model had to be adjusted to the experiments to yield to a result close to the experiments.     

A coupled edge-/face-based smoothed finite element method for structural-acoustic problems

The edge-based smoothed finite element method (ES-FEM) and the face-based smoothed finite element method (FS-FEM) developed recently have shown great efficiency in solving solid mechanics problems with triangular and tetrahedral meshes. In this paper, a coupled ES-/FS-FEM model is extended to solve the structural-acoustic problems consisting of a plate structure interacting with the fluid medium. Three-node triangular elements and four-node tetrahedral elements are used to discretize the two-dimensional (2D) plate and three-dimensional (3D) fluid, respectively, as they can be generated easily and even automatically for complicated geometries. The field variable in each element is approximated using the linear shape functions, which is exactly the same as that in the standard FEM. The gradient field of the problem is obtained particularly using the gradient smoothing operation over the edge-based and face-based smoothing domains in 2D and 3D, respectively. The gradient smoothing technique can provide a proper softening effect to the model, effectively solve the problems caused by the well-known “overly-stiff” phenomenon existing in the standard FEM, and hence significantly improve the accuracy of the solution for the coupled systems. Intensive numerical studies have been conducted to verify the effectiveness of the coupled ES-/FS-FEM for structural-acoustic problems.     

Active modal control simulation of vibro-acoustic response of a fluid-loaded plate

Active modal control simulation of vibro-acoustic response of a fluid-loaded plate is presented. The active modal control of the vibro-acoustic response is implemented using piezoelectric actuators/sensors. The active modal damping is added to the coupled system via negative velocity feedback. The feedback gain between the piezoelectric actuators/sensors for the modal control is obtained using the in-vacuo modal matrix and the incompressible fluid-loaded modal matrix. The modal control performance of structural vibration and acoustic radiation of a baffled plate is numerically studied. It is shown that the proposed method increases the modal damping ratio and achieves reduction in the mean square velocity and the sound power for given modes of the fluid-loaded plate.     

Applied topology optimization of vibro-acoustic hearing instrument models

Designing hearing instruments remains an acoustic challenge as users request small designs for comfortable wear and cosmetic appeal and at the same time require sufficient amplification from the device. First, to ensure proper amplification in the device, a critical design challenge in the hearing instrument is to minimize the feedback between the outputs (generated sound and vibrations) from the receiver looping back into the microphones. Secondly, the feedback signal is minimized using time consuming trial-and-error design procedures for physical prototypes and virtual models using finite element analysis. In the present work it is demonstrated that structural topology optimization of vibro-acoustic finite element models can be used to both sufficiently minimize the feedback signal and to reduce the time consuming trial-and-error design approach. The structural topology optimization of a vibro-acoustic finite element model is shown for an industrial full scale model hearing instrument.     

A 3D state-space solution for free-vibration analysis of a radially polarized laminated piezoelectric cylinder filled with fluid

This paper presents a three-dimensional exact mixed state-space solution for the free-vibration analysis of simply-supported arbitrarily thick laminated piezoceramic hollow cylinders completely filled with fluid. The piezoelectric layers of the laminated cylinder are supposed to be polarized in the radial direction and the fluid is considered inviscid and compressible. This exact solution and the corresponding results can be used to develop accurate piezoelectric shell finite elements, and to investigate the effects of various parameters on the natural frequencies and mode shapes of the fluid/piezoelectric-structure coupled system.     

一种分析周期加筋板声辐射的高效方法

为了研究周期加筋板的声辐射特性,建立了一种计算水中周期加筋板在简谐点力作用下的远场辐射声压的高效方法。该方法借助于傅里叶变换法只要先将耦合系统的声振方程,加强筋的弯曲和扭转运动方程,声学波动方程和耦合边界条件转换到波数域中,联合求解得到一组关于平板横向位移的无限大耦合代数方程组,再将该方程组截断成有限大小由数值方法求出波数域中的位移响应,便可结合稳相法得到远场辐射声压。与现有方法给出的结果对比发现二者完全吻合,验证了本文方法的有效性;通过数值方法研究了激励力位置、板厚,加强筋间距和宽度对周期加筋板声辐射特性的影响,得到了具有实际意义的结论。      

Vibro-acoustic modelling of a railway bridge crossed by a train

This paper presents a vibro-acoustic modelling of a railway bridge excited by a moving train. The modelling of the bridge-train system is carried out by the modal superposition method taking into account the train mass, the viscoelastic suspension of the vehicles with an unlimited number of trucks and spans of the bridge. The numerical resolution of the coupled equations of motion is carried out by the Newmark’s method with an iterative process. we studied on one hand the influence of the track irregularities on the dynamic behaviour of the bridge-train system on the other hand the noise radiated by the bridge due to the passage of the train. The acoustic pressure is obtained by solving the wave equation which has as excitations source the bridge acceleration, they are considered as acoustic monopoles.     

含损伤黏弹性阻尼加筋层合板声功率和指向性变异*

该文旨在研究损伤位置和程度对自由阻尼加筋层合板声辐射功率和指向性的影响。基于Mindlin和Timoshenko梁理论,建立了自由阻尼层合板-梁组合结构有限元模型。数值求解四边简支边界条件自由阻尼加筋层合板振动响应,继而通过Rayleigh积分计算加筋层合板辐射声功率和指向性。将计算得到的前4阶模态固有频率、声辐射功率与指向性与已有文献进行了对比基本一致,验证了数值模型的正确性。最后,详细讨论了损伤位置和程度对自由阻尼加筋层合板固有频率、振型、声辐射功率和指向性的影响,结果表明：随着结构损伤程度的增大,声辐射功率峰值向低频移动,在更多角度上出现明显的指向性;声辐射功率和指向性对损伤位置比损伤程度更加敏感。     

Accurate free vibration analysis of thick laminated circular plates with attached rigid core

This paper deals with the free vibration behavior of laminated transversely isotropic circular plates with axisymmetric rigid core attached at the center. The governing equations of motion are obtained based on Mindlin's first-order shear deformation plate theory. Two possible categories of vibration modes related to up-down translation of the core and wobbly rotation of the core about a diameter are studied. Accurate natural frequencies hitherto not reported in the literature are presented for a wide range of thickness-to-radius ratio, inner-to-outer radius ratio, mass and moment of inertia ratios of the core and various boundary conditions at the outer edge of the plate. Numerical results are compared with those of a three-dimensional finite element method (3-D FEM) to demonstrate the high accuracy and reliability of the current analysis.     

三维浅海下弹性结构声辐射预报的有限元-抛物方程法

利用多物理场耦合有限元法对结构和流体适应性强、抛物方程声场计算高效准确的特点,提出了三维浅海波导下弹性结构声振特性研究的有限元-抛物方程法.该方法采用多物理场耦合有限元理论建立浅海下结构近场声辐射模型,计算局域波导下结构声振信息,并提取深度方向上复声压值作为抛物方程初始值;然后采用隐式差分法求解抛物方程以步进计算结构辐射声场.重点介绍了该方法对浅海下结构声辐射计算的准确性、高效性以及快速收敛性后,对Pekeris波导中有限长弹性圆柱壳的声振特性进行了分析.研究得出,当圆柱壳靠近海面(海底)时,其耦合频率比自由场下的要高(低),当潜深达到一定范围时,与自由场耦合频率基本趋于一致;在低频远场,结构辐射场与同强度点源声场具有一定的等效性,且等效距离随着频率增加而增加;由于辐射声场受结构振动模态、几何尺寸和简正波模式影响,结构辐射场传播的衰减规律按近场声影响区、球面波衰减区、介于球面波和柱面波衰减区、柱面波衰减区四个扩展区依次进行.