Coupled FEM/BEM for control of noise radiation and sound transmission using piezoelectric shunt damping

In this paper, we present a coupled finite element/boundary element method (FEM/BEM) for control of noise radiation and sound transmission of vibrating structure by passive piezoelectric techniques. The system consists of an elastic structure (with surface mounted piezoelectric patches) coupled to external/internal acoustic domains. The passive shunt damping strategy is employed for vibration attenuation in the low frequency range. The originality of the present paper lies in evaluating the classically used FEM/BEM methods for structural–acoustics problems when taking account smart systems at the fluid–structure interfaces.     

Placement and dimension optimization of shunted piezoelectric patches for vibration reduction

Passive structural vibration reduction by means of shunted piezoelectric patches is addressed in this paper. We present a strategy to optimize, in terms of damping efficiency, the geometry of piezoelectric patches as well as their placement on the host elastic structure. This procedure is based on the maximization of the modal electro-mechanical coupling factor (MEMCF) of the mechanical vibration mode to which the shunt is tuned. To illustrate the method, a general analytical model of a laminated beam is proposed. Two particular configurations are investigated: (i) a beam with two collocated piezoelectric patches connected in series or in parallel to the shunt and (ii) a cantilever beam with one patch. After a modal expansion, original closed-form solutions of the MEMCF are exhibited, which enables to compute optimal values for the placement, length and thickness of the piezoelectric patches that maximize the MEMCF. A dimensionless model is used so that this study can be used to design any smart beam, whatever be its dimensions. More general results about the coupling mechanisms between the piezoelectric patches and the host structure are also raised. In particular, it is found that the patches thickness is an essential parameter and that several configurations are possible, depending on the considered vibration mode. Experiments are also proposed to validate the model.     

应用长度极化压电陶瓷33模态的 半主动减振技术研究*

本文提出利用长度方向极化的压电材料的33模态来实现半主动减振。论文以横梁为例,通过理论分析和有限元仿真,对比研究了当压电材料分别连接31, 33两种模态对应的最佳分流电路时,压电材料两种模态在横梁的共振频率附近的减振效果。结果表明33模态比31模态具有更高的减振效率。此外,鉴于33模态存在极化长度有限的问题,仿真分析了压电材料的尺寸和位置对减振效果的影响。在此基础之上,提出了一个利用压电材料33模态的多模态减振的组合设计,对横梁的前三个模态起到了很好地减振作用。相对31模态而言,横梁的每个振动模态均有约15dB的减振提升。     

复式降噪块地铁车轮减振降噪特性

为探究一种复式降噪块装置及其组合形式对某S型辐板地铁车轮的减振降噪效果和机理,在半消声室内,分别对1种自由状态下的标准车轮和3种形式的复式降噪块车轮开展阻尼特性及振动声辐射特性试验,并通过有限元建模对其进行了模态计算。结果表明:复式降噪块装置可在全频段内提高车轮阻尼比,并对车轮各部位有良好的减振效果,以轮辋和踏面的减振效果最为显著;其中,6个制振阻尼片形式的降噪块对车轮的降噪效果最显著,径向激励下的降噪量为13.1 dB(A),轴向激励下的降噪量为11.1 dB(A),降噪频段主要集中在1000 Hz以上中高频。该文研究结果是对列车降噪研究领域的补充和发展。     

ITER聚变装置重力支撑有限元模态分析

运用有限元分析软件ANSYS建立了ITER装置重力支撑结构环向20°的三维有限元模型,采用子空间法对ITER重力支撑结构系统进行了有限元模态分析,求出了重力支撑系统的前10阶固有频率和振型,并对振型特点进行了分析。     

Identification of the piezoelectric material coefficients using the finite element method with an asymptotic waveform evaluation

A rapid identification of the piezoelectric material constants for a piezoelectric transducer is proposed. The validity of a three-dimensional finite element routine was confirmed experimentally. The asymptotic waveform evaluation (AWE) was adopted for a fast frequency sweep of the finite element analysis. The three-dimensional finite element method with an AWE and a design sensitivity method was used for a material inversion scheme of piezoelectric transducers. In order to confirm the inversion routine of the material constants, the mechanical displacements, which mean the mode shape, were calculated along the vertical and lateral position of the sample transducer.     

Finite element analysis of nano-scale Timoshenko beams using the integral model of nonlocal elasticity

Stress-strain relation in Eringen's nonlocal elasticity theory was originally formulated within the framework of an integral model. Due to difficulty of working with that integral model, the differential model of nonlocal constitutive equation is widely used for nanostructures. However, paradoxical results may be obtained by the differential model for some boundary and loading conditions. Presented in this article is a finite element analysis of Timoshenko nano-beams based on the integral model of nonlocal continuum theory without employing any simplification in the model. The entire procedure of deriving equations of motion is carried out in the matrix form of representation, and hence, they can be easily used in the finite element analysis. For comparison purpose, the differential counterparts of equations are also derived. To study the outcome of analysis based on the integral and differential models, some case studies are presented in which the influences of boundary conditions, nonlocal length scale parameter and loading factor are analyzed. It is concluded that, in contrast to the differential model, there is no paradox in the numerical results of developed integral model of nonlocal continuum theory for different situations of problem characteristics. So, resolving the mentioned paradoxes by means of a purely numerical approach based on the original integral form of nonlocal elasticity theory is the major contribution of present study.     

Numerical and experimental studies on housing optimization for noise reduction of an axial piston pump

This paper presents a methodology to reduce the noise of an axial piston pump through modification of the housing structure, combined with both numerical and experimental methods. The finite element models of the housing and cover are established, and are assembled together. The finite element models are validated and updated using experimental modal analysis. The frequency response function of the assembly is calculated, and the shell element in the inner surfaces of the housing is added. The effects of the thickness of the shell element on the frequency response function are identified. A topology optimization is conducted for the purpose of reducing the frequency response function and the increase of mass. The prototype pump is manufactured and assembled. Different experimental measurements are carried out, including the measurement of the vibration and the distributions of the sound pressure levels around the pump. Results show that the vibration and noise are reduced by using the optimized housing. In particular, the average sound pressure level is reduced by about 2 dB(A) at the discharge pressure of 250 bar, and the sound pressure level at the second harmonic is reduced significantly. The method proposed here can also be used for other kinds of displacement pumps.     

Spatial and temporal thermal analysis of acousto-optic deflectors using finite element analysis model

Thermal effects greatly influence the optical properties of the acousto-optic deflectors (AODs). Thermal analysis plays an important role in modern AOD design. However, the lack of an effective method of analysis limits the prediction in the thermal performance. In this paper, we propose a finite element analysis model to analyze the thermal effects of a TeO₂-based AOD. Both transducer heating and acoustic absorption are considered as thermal sources. The anisotropy of sound propagation is taken into account for determining the acoustic absorption. Based on this model, a transient thermal analysis is employed using ANSYS software. The spatial temperature distributions in the crystal and the temperature changes over time are acquired. The simulation results are validated by experimental results. The effect of heat source and heat convection on temperature distribution is discussed. This numerical model and analytical method of thermal analysis would be helpful in the thermal design and practical applications of AODs.     

Suppression of brake squeal noise applying finite element brake and pad model enhanced by spectral-based assurance criteria

An enhanced dynamic finite element (FE) model with friction coupling is applied to analyze the design of disc brake pad structure for squeal noise reduction. The FE model is built-up from the individual brake component representations. Its interfacial structural connections and boundary conditions are determined by correlating to a set of measured frequency response functions using a spectral-based assurance criterion. The proposed friction coupling formulation produces an asymmetric system stiffness matrix that yields a set of complex conjugate eigenvalues. The analysis shows that eigenvalues possessing positive real parts tend to produce unstable modes with the propensity towards the generation of squeal noise. Using a proposed lumped parameter model and eigenvalue sensitivity study, beneficial pad design changes can be identified and implemented in the detailed FE model to determine the potential improvements in the dynamic stability of the system. Also, a selected set of parametric studies is performed to evaluate numerous design concepts using the proposed dynamic FE model. The best pad design attained, which produces the least amount of squeal response, is finally validated by comparison to a set of actual vehicle test results.     

Regression curves for vibration transmission across junctions of heavyweight walls and floors based on finite element methods and wave theory

Sound insulation prediction models in European and International Standards use the vibration reduction index to calculate flanking transmission across junctions of walls and floors. These standards contain empirical relationships between the ratio of mass per unit areas for the walls/floors that form the junction and a frequency-independent vibration reduction index. However, calculations using wave theory show that there is a stronger relationship between the ratio of characteristic moment impedances and the transmission loss from which the vibration reduction index can subsequently be calculated. In addition, the assumption of frequency-independent vibration reduction indices has been shown to be incorrect due to in-plane wave generation at the junction. Therefore numerical experiments with FEM, SFEM and wave theory have been used to develop new regression curves between these variables for the low-, mid- and high-frequency ranges. The junctions considered were L-, T- and X-junctions formed from heavyweight walls and floors. These new relationships have been implemented in the prediction models and they tend to improve the agreement between the measured and predicted airborne and impact sound insulation.     

Development of a finite element model for coupled radiative and conductive heat transfer in participating media

Considering the geometrical applicability, a finite element model (FEM) for coupled radiative-conductive heat transfer has been developed which is applicable to enclosures of arbitrary geometry in present research. The present work provides a solution of coupled heat transfer in a rectangular, cylindrical or annulus enclosure with black or gray walls containing an absorbing-emitting-scattering medium. It is also applied to study the influence of conductive/radiation coefficient, albedo and wall emissivity on the temperature distribution in the medium. Compared with the results available in other references, the present FEM has no limitation with respect to geometry and can predict the coupled radiative-conductive heat transfer in participating media accurately.     

Finite element formulation of the first- and second-order discrete ordinates equations for radiative heat transfer calculation in three-dimensional participating media

Two finite element methods (FEMs), FEDOM1 and FEDOM2 (standing for the first and the second finite element discrete ordinates methods, respectively), are formulated and numerically tested. The reference second-order discrete equation is modified in its scattering terms and is applied to the problems of absorbing/emitting and anisotropically scattering media by using the FEM. Numerical features of the developed FEMs are compared with one of the discrete ordinates interpolation method (DOIM), which uses a finite difference scheme. Prediction results of radiative heat transfer by these two FEMs are compared with reference solutions and verified in three-dimensional enclosures containing participating media. The results of FEDOM1 and FEDOM2 agree well with exact solutions for the problem of absorbing/emitting medium with various range of optical thickness. Generally, the two FEMs show more accurate results than DOIM. And FEDOM1 shows more accurate results than FEDOM2 in most of the test problems. Both of the developed FEMs show reasonable results compared with published Monte Carlo solutions for the tested absorbing/emitting and anisotropically scattering media. Although the FEDOM2 is not as accurate as the FEDOM1, it shows its own advantages that it reduces CPU time and memory space of dependent variable to half.