双层板腔结构声传输及其有源控制研究

利用子系统模态综合方法,结合阻抗-导纳矩阵法,建立了双层板腔结构向自由空间声传输及其在入射板PZT控制、辐射板PZT控制,和腔中次级声源作动等多种控制策略下,系统物理模型的统一的分析模型,导出了系统模态响应及最优次级源强度的统一的阻抗-导纳矩阵表达式。该模型表达式各部分物理意义清晰、明确,便于进行系统耦合理论、有源控制及其机理的分析和数值研究。然后,在此基础上对双层板腔结构声传输有源控制进行了全面深入的数值计算和分析研究,重点探讨了控制方法策略及系统参数对有源控制效果的影响及其对应的控制机理。结果表明:入射板PZT作动辐射声功率最小控制策略是通过入射板、声腔和辐射板三个子系统的模态抑制或重组达到消声的目的,涉及多种复杂控制机理,对入射板、辐射板和声腔模态均有效,但对入射板模态更有效;在低频段声腔(0,0,0)模态在系统耦合响应中起主导作用,因此利用腔中次级声源作动能获得较理想的控制效果,是一种较好的控制策略;由于声腔模态与结构模态间复杂的耦合关系,使得某些频率处腔中声势能一定程度上的降低并不一定导致系统声传输损失的增加,因此,腔中声势能最小控制策略不一定能够获得理想的声传输控制效果。      

矩形封闭声腔壁板轻量化对声固耦合特性的影响

基于模态耦合法建立了考虑对侧柔性壁板的矩形封闭腔体声固耦合模型,导出了耦合系统声振响应随柔性板材料属性及厚度变化的近似关系.通过数值仿真计算,详细分析了单柔性板-单侧激励、双柔性板-双侧激励及双柔性板-单侧激励三种情况下板的轻量化设计对系统声固耦合特性及腔内声压响应的影响.结果表明:对于单柔性板-单侧激励及双柔性板-双侧激励情况,低频段腔内声压主要取决于板厚,其次是杨氏模量,而与板密度关系较弱.因此使用适当增厚的轻质板可以同时达到减重和低频区降噪的目标.对于双柔性板-单侧激励情况,适当的轻量化设计可以显著增强两板间低频段振动的耦合,从而降低该频段的声腔模态响应及腔内噪音.在中高频段,增加板厚和材料密度对降低三种情况的腔内声压均有利。      

Modeling and Measurement of a Tunable Acoustoelastic System

Acoustoelastic coupling occurs when a hollow structure’s in-vacuo mode aligns with an acoustic mode of the internal cavity. The impact of this coupling on the total dynamic response of the structure can be quite severe depending on the similarity of the modal frequencies and shapes. Typically, acoustoelastic coupling is not a design feature, but rather an unintended result that must be remedied as modal tests of structures are often used to correlate or validate finite element models of the uncoupled structure. Here, however, a test structure is intentionally designed such that multiple structural and acoustic modes are well-aligned, resulting in a coupled system that allows for an experimental investigation. First, coupling in the system is identified using a measure termed the magnification factor. Next, the structural-acoustic interaction is measured. Modifications to the system demonstrate the dependency of the coupling on changes in the mode shape and frequency proximity. This includes an investigation of several practical techniques used to decouple the system by altering the internal acoustic cavity, as well as the structure itself. These results show that acoustic absorption material effectively decoupled the structure while structural modifications, in their current form, proved unsuccessful. Readily available acoustic absorptive material was effective in reducing the coupled effects while presumably adding negligible mass or stiffness to the structure.     

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。      

New modeling method and mechanism analyses for active control of interior noise in an irregular enclosure using piezoelectric actuators

A new modeling method is developed in this paper for the active minimization of noise within a three-dimensional irregular enclosure using distributed lead zirconate titanate piezoelectric (PZT) actuators, and the control mechanisms for irregular enclosure are analyzed. The irregular enclosure is modeled with four rigid walls and two simply supported flexible panels, and PZT actuators are bound to one of the flexible panels. The process of the new modeling method is as follows. First, the modal coupling method is used to establish the motion equations, which contain important coefficients such as modal masses and modal coupling coefficients, etc., of acoustic-structural-piezoelectric coupling system. Then, the acoustic modes and the modal masses of irregular enclosure are calculated by numerical methods. Last, the modal coupling coefficients in motion equations are calculated according to the numerical results of the acoustic modes of irregular enclosure and the modes of two panels. The validity of this modeling method is verified by a regular hexahedron enclosure. Two cost functions are applied to this model. With the two cost functions, good results are obtained in minimizing the sound-pressure level (SPL) within irregular enclosure according to numerical investigations. By comparing the results obtained under controlled and uncontrolled states, the control mechanisms of the system are discussed. It is found that the control mechanisms vary with disturbance frequencies. At most disturbance frequencies, the SPL within enclosure is reduced by restructuring the modes of two panels simultaneously. When the disturbance frequency comes close to one of the natural frequencies of panel a, the dominant mode of panel a is suppressed, while the modes of panel b are reconstructed. While the disturbance frequency is near one of the natural frequencies of panel b, the modes of two panels are restructured at the same time.     

Vibro-acoustic analysis of a rectangular cavity bounded by a flexible panel with elastically restrained edges

A coupled system consisting of an acoustic cavity and an elastic panel is a classical problem in structural acoustics and is typically analyzed using modal approaches based on in vacuo structural modes and the rigidly walled acoustic modes which are pre-determined based on separate component models. Such modeling techniques, however, tend to suffer the following drawbacks or limitations: (a) a panel is only subjected to ideal boundary conditions such as the simply supported, (b) the coupling between the cavity and panel is considered weak, and (c) the particle velocity cannot be correctly predicted from the pressure gradient on the contacting interface, to name a few. Motivated by removing these restrictions, this paper presents a general method for the vibro-acoustic analysis of a three-dimensional (3D) acoustic cavity bounded by a flexible panel with general elastically restrained boundary conditions. The displacement of the plate and the sound pressure in the cavity are constructed in the forms of standard two-dimensional and 3D Fourier cosine series supplemented by several terms introduced to ensure and accelerate the convergence of the series expansions. The unknown expansions coefficients are treated as the generalized coordinates and determined using the Rayleigh-Ritz procedure based on the energy expressions for the coupled structural acoustic system. The accuracy and effectiveness of the proposed method are demonstrated through numerical examples and comparisons with the results available in the literature.     

Virtual sensors for active noise control in acoustic-structural coupled enclosures using structural sensing: part II--Optimization of structural sensor placement

The work proposed an optimization approach for structural sensor placement to improve the performance of vibro-acoustic virtual sensor for active noise control applications. The vibro-acoustic virtual sensor was designed to estimate the interior sound pressure of an acoustic-structural coupled enclosure using structural sensors. A spectral-spatial performance metric was proposed, which was used to quantify the averaged structural sensor output energy of a vibro-acoustic system excited by a spatially varying point source. It was shown that (i) the overall virtual sensing error energy was contributed additively by the modal virtual sensing error and the measurement noise energy; (ii) each of the modal virtual sensing error system was contributed by both the modal observability levels for the structural sensing and the target acoustic virtual sensing; and further (iii) the strength of each modal observability level was influenced by the modal coupling and resonance frequencies of the associated uncoupled structural/cavity modes. An optimal design of structural sensor placement was proposed to achieve sufficiently high modal observability levels for certain important panel- and cavity-controlled modes. Numerical analysis on a panel-cavity system demonstrated the importance of structural sensor placement on virtual sensing and active noise control performance, particularly for cavity-controlled modes.     

Experimental validation of a collocated PVDF volume velocity sensor/actuator pair

The active control of sound transmission through a rectangular panel is experimentally verified. The control system is based on a collocated volume velocity sensor/actuator pair which measures and excites the first radiation mode of the panel. Suppression of the first radiation mode is an efficient strategy to control the low frequency sound radiation from the panel. This configuration leads to a simple single-input single-output control system, to which feedback control can be applied.Two implementations of the volume velocity sensor/actuator pair are tested. First, a polyvinyledene fluoride polymer (PVDF) volume velocity actuator foil with shaped electrodes is used in combination with an identical PVDF volume velocity sensor foil. Due to the mechanical coupling between the PVDF sensor and actuator foil, it is shown that a direct velocity feedback control scheme is not feasible because higher order structural modes will be destabilized. Instead integral force feedback is applied, such that the open-loop transfer function has a roll-off towards higher frequencies. Experiments show that this control strategy results in a reduction of the sound pressure in the receiving room of 10 dB at the first structural resonance without spillover to higher order modes. Due to the roll-off towards high frequencies, the control over higher order modes remains limited. Second, a discrete volume velocity sensor is constructed by summing the signals from 12 point sensors placed on the panel. The volume velocity actuator consists of two PVDF foils, glued on each side of the panel and driven in opposite phase. Direct volume velocity feedback is applied to this system, which is minimum phase. This control system is capable of reducing the sound pressure in the receiving room below 300 Hz by 10-15 dB without spillover to higher order modes.     

Reduction of sound transmission into a circular cylindrical shell using distributed vibration absorbers and Helmholtz resonators

A modal expansion method is used to model a cylindrical enclosure excited by an external plane wave. A set of distributed vibration absorbers (DVAs) and Helmholtz resonators (HRs) are applied to the structure to control the interior acoustic levels. Using an impedance matching method, the structure, the acoustic cavity, and the noise reduction devices are fully coupled to yield an analytical formulation of the structural kinetic energy and acoustic potential energy of a treated cylindrical cavity. Lightweight DVAs and small HRs tuned to the natural frequencies of the targeted structural and acoustic modes, respectively, result in significant acoustic and structural attenuation when the devices are optimally damped. Simulations show that significant interior noise reduction can only be achieved by adding damping to both structural and acoustic modes, which are resonant in the frequency bandwidth of interest. In order to be independent of the azimuth angle of the excitation and to avoid unwanted modal interactions, the devices are distributed evenly around the cylinder in rings. This treatment can only achieve good performance if the structure and the acoustic cavity are lightly damped.     

Free vibration analysis of a rotating hub–functionally graded material beam system with the dynamic stiffening effect

A comprehensive dynamic model of a rotating hub–functionally graded material (FGM) beam system is developed based on a rigid–flexible coupled dynamics theory to study its free vibration characteristics. The rigid–flexible coupled dynamic equations of the system are derived using the method of assumed modes and Lagrange's equations of the second kind. The dynamic stiffening effect of the rotating hub–FGM beam system is captured by a second-order coupling term that represents longitudinal shrinking of the beam caused by the transverse displacement. The natural frequencies and mode shapes of the system with the chordwise bending and stretching (B–S) coupling effect are calculated and compared with those with the coupling effect neglected. When the B–S coupling effect is included, interesting frequency veering and mode shift phenomena are observed. A two-mode model is introduced to accurately predict the most obvious frequency veering behavior between two adjacent modes associated with a chordwise bending and a stretching mode. The critical veering angular velocities of the FGM beam that are analytically determined from the two-mode model are in excellent agreement with those from the comprehensive dynamic model. The effects of material inhomogeneity and graded properties of FGM beams on their dynamic characteristics are investigated. The comprehensive dynamic model developed here can be used in graded material design of FGM beams for achieving specified dynamic characteristics.     

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.     

Radiation from modes of a rectangular panel into a coupled fluid layer

Modal radiation efficiencies are evaluation for a rectangular panel which is simply supported in an infinite baffle and coupled to a fluid layer. The analysis is based on the calculation of the acoustic power radiated into the layer by the panel vibrating in one of its in vacuo natural modes. At low frequencies, the efficiency is inversely proportional to the layer depth; at high frequencies, it exhibits a complex, multiple peak characteristic, associated with the acoustic field of the layer. Comparison with the modal radiation efficiencies of a panel coupled to a fluid half-space shows a similar dependence on mode order and panel dimensions.     

Effects of the inclination of a rigid wall on the free vibration characteristics of acoustic modes in a trapezoidal cavity

The coupling between rigid-walled modes of a rectangular cavity (RC modes) is used to obtain the shapes and resonance frequencies of rigid-walled modes of a trapezoidal cavity (TC modes) with an inclined rigid wall. A method is established to identify the TC modes, where the modes can be defined to evolve from individual RC modes. The wall inclination generates two coupling mechanisms, namely, the local coupling where the RC modes couple at the inclined wall, and the global coupling where the RC modes couple throughout the trapezoidal volume. The latter arises from the nonorthogonality of the RC modes in the trapezoidal volume. Both couplings are selective that only RC modes with the same number of nodes in the direction perpendicular to the inclination are coupled to each other. For small inclinations, each TC mode possesses the distorted shape of the RC mode that evolves it. When the inclination is increased, the TC-mode shape becomes complicated and unrecognizable, and extrema can also exist in the resonance frequency of the TC mode. These behaviors are determined by the behaviors of the local and global couplings of the RC mode. This paper provides an understanding of how the free vibration characteristics of TC modes change with the inclination and what determines these changes.     

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.     

Analysis of the modal energy distribution of an excited vibrating panel coupled with a heavy fluid cavity by a dual modal formulation

This paper describes the modal interaction between a panel and a heavy fluid cavity when the panel is excited by a broad band force in a given frequency band. The dual modal formulation (DMF) allows describing the fluid–structure coupling using the modes of each uncoupled subsystem. After having studied the convergence of the modal series on a test case, we estimate the modal energies and the total energy of each subsystem. An analysis of modal energy distribution is performed. It allows us to study the validity of SEA assumptions for this case. Added mass and added stiffness effects of the fluid are observed. These effects are related to the non-resonant acoustic modes below and above the frequency band of excitation. Moreover, the role of the spatial coupling of the resonant cavity modes with the non-resonant structure modes is also highlighted. As a result, the energy transmitted between the structure and the heavy fluid cavity generally cannot be deduced from the SEA relation established for a light fluid cavity.     

A modal test method using sound pressure transducers based on vibro-acoustic reciprocity

A modal test method that uses sound pressure transducers at fixed locations and an impact hammer roving over a test structure is developed in this work. Since sound pressure transducers are used, the current method deals with a coupled structural–acoustic system. Based on the vibro-acoustic reciprocity, the method is equivalent to one, where acoustic excitations at fixed locations are given and the resulting acceleration of the test structure is measured. The current method can eliminate mass loading due to use of accelerometers, which can destroy existence of repeated or close natural frequencies of a symmetric structure. It can also avoid effects of a nodal line of a mode and an inactive area of a local mode, and measure all the out-of-plane modes within a frequency range of interest, including global and local ones. The coupling between the structure and the acoustic field in a structural–acoustic system introduces asymmetry in the model formulation. An equivalent state space formulation is used for a damped structural–acoustic system and the associated eigenvalue problem is derived. The biorthonormality relations between the left and right eigenvectors and the relations between the structural and acoustic components in the left and right eigenvectors are proved. The frequency response functions associated with the current method are derived and their physical meanings are explained. The guidelines for using the current method, including the types of structures that are suitable for the method, the positions of the sound pressure transducers, and the orientation of the test structure relative to the transducers, are provided. Modal tests were carried out on an automotive disk brake using the traditional and current methods, where multiple accelerometers and microphones were used to measure its dynamic responses induced by impacts, respectively. The differences between the measured natural frequencies using the current method and those from the finite element model of the disk brake are less than 3 percent for the first 18 elastic modes, and the modal assurance criterion values of the associated mode shapes are all above 90 percent. The current method was also used to measure the natural frequencies, damping ratios, and mode shapes of a light circuit board.     

A parametric multi-body section model for modal interactions of cable-supported bridges

A parametric section model is formulated to synthetically describe the geometrically nonlinear dynamics of cable-stayed and suspended bridges through a planar elastic multi-body system. The four-degrees-of-freedom model accounts for both the flexo-torsional motion of the bridge deck and for the transversal motion of a pair of hangers or stay cables. After linearization around the pre-stressed static equilibrium configuration, the coupled equations of motion governing the global deck dynamics and the local cable motion are obtained. A multi-parameter perturbation method is employed to solve the modal problem of internally resonant systems. The perturbation-based modal solution furnishes, first, explicit formulae for the parameter combinations which realize the internal resonance conditions and, second, asymptotic approximations of the resonant frequencies and modes. Attention is focused on the triple internal resonance among a global torsional mode of the deck and two local modes of the cables, due to the relevant geometric coupling which maximizes the modal interaction. The asymptotic approximation of the modal solution is found to finely describe the multiple veering phenomenon which involves the three frequency loci under small variation of the most significant mechanical parameters, including terms of structural coupling or disorder. Moreover, the veering amplitude between any two of the three frequency loci can be expressed as an explicit parametric function. Finally, the disorder is recognized as the only parameter governing a complex phenomenon of triple modal hybridization involving all the resonant modes. The entire hybridization process is successfully described by an energy-based localization factor, presented in a new perturbation-based form, valid for internally resonant system.     

Experimental study of AO and T1 modes of the concert harp

String instruments are usually composed of a set of strings, a soundboard, and a soundbox with sound holes, which is generally designed to increase the sound level by using the acoustic resonances of the cavity. In the case of the harp, the soundbox and especially the sound holes are primarily designed to allow access to the strings for their mounting. An experimental modal analysis, associated to measurements of the acoustic velocity in the holes, shows the importance of two particular modes labeled A0 and T1 as it was done for the guitar and the violin. Their mode shapes involve coupled motions of the soundboard's bending and of the oscillations of the air pistons located in the sound holes. The A0 mode is found above the frequency of the lowest acoustically significant structural mode T1. Thus, the instrument does not really take advantage of the soundbox resonance to increase its radiated sound in low frequencies. However, contribution of mode A0 is clearly visible in the response of the instrument, confirming the importance of the coupling between the soundboard and the cavity.     

某稳瞄转塔结构的有限元模态分析与试验验证

结构动态效应是影响稳瞄系统稳定精度的关键因素。目前有限元模态分析与试验模态分析结合的方法是分析结构动力学特性的最有效途径之一。以某型稳瞄具两轴四框架结构为研究对象,首先利用有限元方法进行了模态预分析。根据仿真结果获取的振型特征,对两轴四框架的外环进行模态测试,给出了前8阶模态的固有频率、振型和模态阻尼比。模态仿真与测试的结果相互验证表明:有限元仿真可实现两轴四框架结构固有频率相对误差小于15%的精度要求,在测点密度足够的条件下振型相关性良好。     

Axion detection with negatively coupled cavity arrays

Using eigenmode analysis and full 3D FEM modelling, we demonstrate that a closed cavity built of an array of elementary harmonic oscillators with negative mutual couplings exhibits a dispersion curve with lower order modes corresponding to higher frequencies. Such cavity arrays may help to achieve large mode volumes for boosting sensitivity of the axion searches, where the mode volume for the composed array scales proportional to the number of elements, but the frequency remains constant. The negatively coupled cavity array is demonstrated with magnetically coupling coils, where the sign of next-neighbour coupling (controlled with their chirality) sets the dispersion curve properties of the resonator array medium. Furthermore, we show that similar effects can be achieved using only positively coupled cavities of different frequencies assembled in periodic cells. This principle is demonstrated for the multi-post re-entrant system, which can be realised with an array of straight metallic rods organised in chiral structures.