Numerical treatment of acoustic problems with the smoothed finite element method

We incorporated a cell-wise acoustic pressure gradient smoothing operation into the standard compatible finite element method and extended the smoothed finite element method (SFEM) for 2D acoustic problems. This enhancement was especially useful for dealing with the problem of an arbitrary shape with violent distortion elements. In this method, the domain integrals that involve shape function gradients can be converted into boundary integrals that involve only shape functions. Restrictions on the shape elements can be removed, and the problem domain can be discretized in more flexible ways. Numerical results showed that the proposed method achieved more accurate results and higher convergence rates than the corresponding finite element methods, even for violently distorted meshes. The most promising feature of SFEM is its insensitivity to mesh distortion. The superiority of the method is remarkable, especially when solving problems that have high wave numbers. Hence, SFEM can be beneficially applied in solving two-dimensional acoustic problems with severely distorted elements, which, in practice, have more foreground than regularity mesh.     

Simulation on laser-induced surface acoustic wave on isotropic cylinders by finite element method

Based on the thermoelastic theory, a finite element model is developed to simulate the process of laser inducing ultrasonic field in isotropic cylinders, which can take the temperature dependence of thermal parameters into account. Using the finite element model, we have simulated the ultrasonic fields induced by a pulse laser line source impacting on the generatrix of aluminum cylinders with different diameters. And the intact waveforms of surface acoustic wave (SAW including cylindrical Rayleigh and Whispering gallery (WG) modes) are presented, which are in very good agreement with the calculated and experimental waveforms in other literatures. Furthermore, the dispersion properties of cylindrical Rayleigh waves are analyzed by the method of phase spectral analysis, and the results show that with the increasing frequency, the phase velocity of cylindrical Rayleigh wave rapidly increases to the maximum value, and then gradually decreases to that of plane Rayleigh wave. With the diameter of cylinder decreasing, the maximum value of phase velocity and the corresponding frequency increase.     

Numerical simulation of laser-generated surface acoustic waves in the transparent coating on a substrate by the finite element method

The optimum finite element model in the system consisting of a transparent coating and an opaque substrate is established based on the analysis of two important parameters: meshing size and time step, and the stability of solution. Taking into account the temperature dependence of material properties, the transient temperature and temperature gradient field are obtained. According to the thermoelastic theory, this temperature gradient field can be taken as a buried bulk source to generate ultrasonic wave. The surface acoustic waves (SAWs) are obtained. The influence of the coating thickness on the SAWs is analyzed. The model provides a useful tool for the determination of modes which are generated by a laser source in transparent coating on opaque substrate. The surface skimming longitudinal wave exists for the multiple oscillations and it charges from unipolar waveforms to dipolar.     

Fast multipole accelerated boundary element method for the Helmholtz equation in acoustic scattering problems

We apply the fast multipole method (FMM) accelerated boundary element method (BEM) for the three-dimensional (3D) Helmholtz equation, and as a result, large-scale acoustic scattering problems involving 400000 elements are solved efficiently. This is an extension of the fast multipole BEM for two-dimensional (2D) acoustic problems developed by authors recently. Some new improvements are obtained. In this new technique, the improved Burton-Miller formulation is employed to over-come non-uniqueness difficultie...     

Circuit-field coupled finite element analysis method for an electromagnetic acoustic transducer under pulsed voltage excitation

This paper presents an analytical method for electromagnetic acoustic transducers (EMATs) under voltage excitation and considers the non-uniform distribution of the biased magnetic field. A complete model of EMATs including the non-uniform biased magnetic field, a pulsed eddy current field and the acoustic field is built up. The pulsed voltage excitation is transformed to the frequency domain by fast Fourier transformation (FFT). In terms of the time harmonic field equations of the EMAT system, the impedances of the coils under different frequencies are calculated according to the circuit-field coupling method and Poynting’s theorem. Then the currents under different frequencies are calculated according to Ohm’s law and the pulsed current excitation is obtained by inverse fast Fourier transformation (IFFT). Lastly, the sequentially coupled finite element method (FEM) is used to calculate the Lorentz force in the EMATs under the current excitation. An actual EMAT with a two-layer two-bundle printed circuit board (PCB) coil, a rectangular permanent magnet and an aluminium specimen is analysed. The coil impedances and the pulsed current are calculated and compared with the experimental results. Their agreement verified the validity of the proposed method. Further- more, the influences of lift-off distances and the non-uniform static magnetic field on the Lorentz force under pulsed voltage excitation are studied.     

超声反射成像测井的有限元分析*

利用有限元方法研究了有限长换能器激发的超声波在套管井多层介质中的传播规律。数值模拟了换能器长度及套管曲率对反射回波的影响。随着换能器长度增加,反射回波频谱谱陷个数由单一向多个变化;套管共振透射窗的反射波相对能量先逐渐减小后振荡变化,较小长度的换能器对套管与水泥环界面的声阻抗区分能力优于较大长度的换能器。随着套管曲率的增大,套管共振透射窗的反射波由单一模式的厚度振动纵波向其他模式波变化。数值模拟结果对超声脉冲反射声波测井仪器的换能器结构优化设计起到了良好的指导作用。     

三维声学多层快速多极子边界元及其应用

快速多极子边界元算法可以加速矩阵和向量乘法运算, 将传统边界元算法的计算量和内存占用量分别降为O(N log²N)和O(N), 适用于大型声学模型模拟计算. 本文发展了一种基于Burton-Miller方程的三维多层声学快速多极子边界元算法. 将新的自适应树状算法应用到对角形式的快速多极子边界元算法, 并使用最新提出的解析式源点矩计算公式, 进一步提高了快速多极子边界元的计算效率. 绝对软球体在内部共振频率处的散射声场计算, 验证了所发展算法在共振频率处求解的正确性. 与Bapat所提供的程序在多脉动球体辐射声场计算精度的比较, 验证了算法及程序在大型模型声学计算中的准确性, 同时显示了其求解的高效性. 最后, 将该算法用于车内声场及水下声学探测的分析计算.     

EAST���ϲ��Ͼ�Ե����������Ԫ����

用有限元法对EAST装置磁体系统的高性能氦气密复合材料绝缘子性能作了全面的分析.结果表明:绝缘子可满足承受EAST装置耐电压15kV的使用要求;热应力对绝缘子的绝缘层影响最大,外力对绝缘层应力的影响可忽略;EAST复合材料绝缘子具有优良的低温力学性能.     

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.     

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.     

随钻声波测井圆弧状压电阵子的有限元分析*

圆弧状压电阵子是随钻声波测井仪发射换能器的核心部件。利用有限元法对圆弧状压电阵子进行了设计分析,结果表明20 kHz以下频率范围内主要存在弯曲振动模态及径向振动模态,且径向振动模态能够满足随钻声波单极测量模式的工作频率要求。针对径向振动模态,数值模拟了几何尺寸对压电阵子声学性能参数的影响。圆弧状压电阵子的谐振频率随着陶瓷片厚度的增大而升高;随着陶瓷片高度、半径及张开角的增大而降低。圆弧状压电阵子的最大发射电压级幅值随着陶瓷片厚度、张开角的增大而降低;随着半径的增大而升高;随着陶瓷片高度的增大,最大发射电压级幅值先升高后逐渐降低。以外径为6.75 in的钻铤为例,最优化设计了圆弧状压电阵子的尺寸,使其满足钻铤模式波隔声阻带中心频率的要求,同时保证了压电阵子具有最大发射电压级。数值模拟结果可以对随钻声波测井仪发射换能器设计起到良好的指导作用。     

Comparison of 1D transfer matrix method and finite element method with tests for acoustic performance of multi-chamber perforated resonator

Multi-chamber perforated resonator (MCPR) is a kind of typical silencer element which can both attenuate broadband noise and satisfy specific installation requirements. The one-dimensional transfer matrix method (TMM) and finite element method (FEM) are widely used to predict the transmission loss of the resonators. This paper mainly focuses on the comparison between 1D TMM and FEM in which detailed perforation modeling is applied for the acoustic modeling of MCPRs. Five resonators with different acoustic attenuation frequency ranges are built for simulation and test. In order to verify the results of the above methods, a transmission loss test facility is designed based on two-load method. Through adjusting the distance between microphones, the facility’s effective measurement frequency can be changed. The results show that despite of the complex modeling and calculation, FEM with detailed perforation modeling shows good consistency with test results in both frequency and amplitude within entire frequency range. In comparison, TMM is limited by the cut-off frequency when calculating transmission losses. Besides, accuracy of TMM in low frequency range is also affected by perforation conditions. However, TMM is time-saving in calculation and structure optimization. In MCPRs’ development process, TMM can be used to quickly design and optimize structure parameters while FEM can be used to verify the acoustic performance before prototyping.     

Stress evaluation of Through-Silicon Vias using micro-infrared photoelasticity and finite element analysis

The Through-SiliconVias (TSV) is a key component of three dimensional electronic packaging. Obtaining its stresses is very important for evaluating its reliability. A micro-infrared photoelasticity system with a thermal loading function was built and applied to characterize the stresses of the TSV structure. Through testing it was found that the stress of each TSV is different even if their fabrication technology is exactly the same, that different TSVs obtain their stress free states at different elevated temperatures, and that their stress free states are maintained even when the temperature is further elevated. A finite element model was used to quantitatively determine the stresses of a TSV under different stress-free temperatures. Different virtual photoelasticity fringe patterns were then created based on the principle of photoelasticity and the simulated stresses. Comparing the virtual fringe patterns with the experimental pattern, an appropriate virtual photoelasticity fringe pattern and the corresponding stresses of TSV were determined     

A non-conforming monolithic finite element method for problems of coupled mechanics

In this study, a Lagrange multiplier technique is developed to solve problems of coupled mechanics and is applied to the case of a Newtonian fluid coupled to a quasi-static hyperelastic solid. Based on theoretical developments in [57], an additional Lagrange multiplier is used to weakly impose displacement/velocity continuity as well as equal, but opposite, force. Through this approach, both mesh conformity and kinematic variable interpolation may be selected independently within each mechanical body, allowing for the selection of grid size and interpolation most appropriate for the underlying physics. In addition, the transfer of mechanical energy in the coupled system is proven to be conserved. The fidelity of the technique for coupled fluid–solid mechanics is demonstrated through a series of numerical experiments which examine the construction of the Lagrange multiplier space, stability of the scheme, and show optimal convergence rates. The benefits of non-conformity in multi-physics problems is also highlighted. Finally, the method is applied to a simplified elliptical model of the cardiac left ventricle.     

Design of a single layer micro-perforated sound absorber by finite element analysis

Micro-perforated sound absorbers with sub-millimeter size holes can provide high absorption coefficients. This paper presents results of work on the development of an effective single layer micro-perforated sound absorber from the commercial composite material Parabeam^® with micro diameter holes drilled on one side. Parabeam^® is used as a structural material made from a fabric woven out of a E-glass yarn and consists of two decklayers bonded together by vertical piles in a sandwich structure with piles (thick fibers) woven into the decklayers. The paper includes, the analytical model developed for prediction of absorption coefficients, finite element solution using commercial software MSC.ACTRAN and experimental results obtained from impedance tube measurements. A simple optimization is performed based on the developed models to obtain an efficient absorber configuration. It has been anticipated that several different and interesting applications can be deduced by combining structural and sound absorption properties of this new micro-perforated absorber.     

Extraction of isotropic points using simulated isoclinics obtained by photoelasticity-assisted finite element analysis

A method for extracting isotropic points in structures using simulated isoclinics obtained from a combination of photoelastic experiments and finite element analysis (FEA) is presented. This method is divided into two parts. The first part involves the confirmation of the boundary condition necessary for FEA using isochromatics obtained by photoelastic experiments. The second part involves the determination of isotropic points using simulated isoclinics obtained by FEA under the boundary condition confirmed by photoelastic experiments. This method is applied to a ring and T-shaped plates subjected to a compressive load. The results show that the isotropic points in the ring and T-shaped plates could be accurately and easily extracted by this method.     

A hybrid finite/boundary element method for periodic structures on non-periodic meshes using an interior penalty formulation for Maxwell’s equations

This paper presents a hybrid finite element/boundary element (FEBE) method for periodic structures. Periodic structures have been efficiently analyzed by solving for a single unit cell utilizing Floquet’s theorem. However, most of the previous works require periodic meshes to properly impose the boundary conditions on the outer surfaces of the unit cell. To alleviate this restriction, the interior penalty method is adopted and implemented in this work. Also, the proper treatment of the boundary element part is addressed to account for the non-conformity of the boundary element mesh. Another ingredient of this work is the use of the efficient boundary element computation, accelerated by the Ewald transformation for the calculation of the periodic Green’s function. Finally, the method is validated through examples which are discretized without the constraint of a periodic mesh.     

小阻尼界面房间声传输函数和声脉冲响应函数的有限元素法

有限元法可用于以声波动方程为基础通过数值计算求解室内声场,适用于分析界面阻抗非均匀分布和复杂形状房间内声场的低频特性。本文首先介绍了小阻尼界面条件下室内声场简正方式、声衰变系数、混响时间的ＦＥＭ计算方法。在此基础上导出了房间内两点之间声传输函数和声脉冲响应函数的ＦＥＭ计算模型,并以矩形房间为例详细讨论了有关细节。本文所讨论的计算模型可以映房间内不同的声源点,接收点位置上的声压频谱特性和脉冲响应的时     

声波测井中的物理问题

文章从声波测井的基本概念入手,介绍了什么是声波测井,其基本原理是什么,声波测井中的主要物理问题是什么,还从几个侧面介绍了声波测井的基本应用和未来的发展趋势,包括传统的电缆测井、目前国外流行的随钻声波测井以及具有应用前景但是尚处于研究阶段的震电测井.文章向从事物理研究的工作者概述了声波测井相关的物理问题和研究的发展现状,为打算涉入声波测井领域研究或者对相关领域研究感兴趣的读者提供了一些基本素材和知识.