旋转点声源声场的数值仿真计算

旋转声源辐射声场的计算是利用点源模型预测风扇离散噪声的关键所在,对叶片式机械气动噪声的研究具有重要参考价值.提供了在任意边界条件下计算旋转点声源辐射卢场的数值仿真计算方法.将连续的旋转声源离散化,处理为分布于旋转轨迹上的有限个固定点声源.利用离散化处理后的声源,通过边界元法分别计算旋转单极子和旋转点力源的辐射声场.在自由空间内的计算结果与理论解进行了对比验证,得到较为理想的结果:另外进行了有限长圆管内旋转点声源辐射声场的数值计算,由此对不同长度圆管的结果进行对比,分析了管道长度对声场分布以及指向性的影响规律.     

Transient scattering of Rayleigh-Lamb waves by a surface-breaking crack: Comparison of numerical simulation and experiment

The transient scattering of Rayleigh-Lamb waves by a surface-breaking crack in a plate is investigated in both time and frequency domains by using the hybrid numerical method which combines the finite element discretization of the vicinity of the crack with the Green's function integral representation of the exterior scattered field. The frequency domain response is obtained by solving a set of large sparse unsymmetric complex matrix equations, elements of which are stored in a compacted data structure, by the biconjugate gradient method. The time domain solution is then obtained by using FFT. The source function generated by a steel ball impact is extracted by a direct integration technique. It is then used to simulate some available experimental results. Good agreement has been obtained. Numerical and experimental results show the effect of the crack more in the near field than far away.     

Modeling of finite-amplitude sound beams: second order fields generated by a parametric loudspeaker

The nonlinear interaction of sound waves in air has been applied to sound reproduction for audio applications. A directional audible sound can be generated by amplitude-modulating the ultrasound carrier with an audio signal, then transmitting it from a parametric loudspeaker. This brings the need of a computationally efficient model to describe the propagation of finite-amplitude sound beams for the system design and optimization. A quasilinear analytical solution capable of fast numerical evaluation is presented for the second-order fields of the sum-, difference-frequency and second harmonic components. It is based on a virtual-complex-source approach, wherein the source field is treated as an aggregation of a set of complex virtual sources located in complex distance, then the corresponding fundamental sound field is reduced to the computation of sums of simple functions by exploiting the integrability of Gaussian functions. By this result, the five-dimensional integral expressions for the second-order sound fields are simplified to one-dimensional integrals. Furthermore, a substantial analytical reduction to sums of single integrals also is derived for an arbitrary source distribution when the basis functions are expressible as a sum of products of trigonometric functions. The validity of the proposed method is confirmed by a comparison of numerical results with experimental data previously published for the rectangular ultrasonic transducer.     

An improved boundary distributed source method for two-dimensional Laplace equations

In this work, the boundary distributed source (BDS) method [EABE 34(11): 914-919] based on the method of fundamental solutions (MFS) is considered for the solution of two-dimensional Laplace equations. The BDS is a truly mesh-free method and quite easy to implement since the source points and field points are collocated on the domain boundary while the conventional MFS requires a fictitious boundary where the source points locate. The main idea of the BDS is that to avoid the singularities of the fundamental solutions the concentrated point sources in the conventional MFS are replaced by distributed sources over circles centered at the source points. In the original BDS, all elements of the system matrix can be derived analytically in a very simple form for the Dirichlet boundary conditions and off-diagonal elements for the Neumann boundary conditions, while the diagonal elements for the Neumann boundary conditions can be obtained indirectly from the constant potential field. This work suggests a simple way to determine the diagonal elements for the Neumann boundary conditions by invoking that the boundary integration of the normal gradient of the potential should vanish. Several numerical examples are addressed to show the feasibility and the accuracy of the proposed method.     

The potential due to a uniform source distribution over a triangular domain

An exact expression is derived for the potential due to a uniform source distribution over a triangular domain. This expression, which is valid for arbitrary field points, is important for the numerical solution of electromagnetic field problems. Numerical values of the potential are calculated by using the expression obtained, and are compared with the results derived by numerical integration.     

双层插值NAH噪声源定位方法研究

针对近场声全息(near-fieldacousticholography,NAH)在实际测量环境下降低环境噪声的影响且保证全息面上声压重建精度的需求,基于空间面积分声压重建理论,在基于等效源法的近场声全息方法(near-field acoustic holography based on equivalent sour...     

Application of early arrival waveform inversion with pseudo-deconvolution misfit function by source convolution

Typical seismic inversion methods require a source wavelet estimated from the data. Inaccurate wavelet estimation may severely undermine the seismic inversion results. We propose a pseudo-deconvolution method that mitigates the requirement for accurate wavelet estimation in early arrival waveform inversion as follows. For a pair of observed and predicted data-sets, we first extract the respective source wavelets from the near-offset part of the two data-sets. Next, we convolve the former data-set with the latter wavelet, and the latter data-set with the former wavelet. The mismatch between these two is then minimized as in standard seismic inversion. Conveniently implemented in the frequency domain, this method is both fast and robust. This is verified by numerical tests on both synthetic and field data.     

Influences of heat source model on welding residual stress and distortion in a multi-pass J-groove joint

Welding mechanical behaviors including residual stress and distortion are highly non-linear phenomena in nature. When numerical simulation methods such as thermal elastic plastic finite element method (FEM) are used to quantitatively predict welding residual stress and distortion, a long computational time is required especially for multi-pass joints. In real engineering structures, many weldments have large dimensions and complex shapes, and they are usually assembled by a multi-pass welding process. Therefore, it is necessary to develop time-effective computational approaches for practice engineering analysis. In this study, a method based on variable length heat sources was proposed for the analysis of thermo-mechanical behaviors for multi-pass joints. The welding residual stress field in a dissimilar metal J-groove joint with axis-symmetric geometrical shape, which was performed by a semi-circle balanced welding process, was investigated using the proposed method. The simulation results were compared with the measured data as well as the simulation results computed by a moving heat source. Meanwhile, the instantaneous line heat source was also employed to estimate the welding residual stresses in the same joint in an extreme case. The influences of heat source model (type) on welding residual stress and distortion were discussed.     

利用源强分布声辐射模态识别噪声源

为了解决噪声源识别中存在的识别精度不高、分辨率受限、对测量条件要求高等问题,提出了基于源强声辐射模态的噪声源识别方法。该方法首先计算结构的源强声辐射模态矩阵和声场分布模态矩阵,然后利用声场中测得的声压数据向量与结构声场分布模态矩阵的关系求出声辐射模态展开系数向量,最后通过声辐射模态矩阵和声辐射模态展开系数向量的积就可得到结构的源强分布,从而达到对噪声源识别的目的。该方法利用较少的测量点可以获得较高分辨率和识别精度。通过平板振动仿真和音箱实验验证了该方法对平面结构噪声源识别的有效性。     

基于压控电荷源和小波变换自适应算法的主-被动压电振动控制

针对压电被动振动方法中电路参数环境适应能力差、电路复杂和压电主动振动方法需要较高的输入功率问题,提出了一种基于压控电荷源和小波变换自适应算法的振动主-被动控制策略。首先,针对压电片等效电路的特点,设计了压控电荷源电路,并阐述了主-被控制方法的控制原理;对于压控电荷源的控制电压,引入了小波变换自适应算法,提高了系统的自适应能力。最后,基于dSPACE实时仿真系统,利用模拟电路和压电元件,设计并建立了四边固支的压电合金板的主-被动振动控制实验平台,对提出的方法进行了正弦和白噪声激励下的振动控制实验研究。结果表明,提出的方法能够有效的抑制压电合金板结构由于正弦激励引起的单模态和多模态振动,且能有效抑制白噪声激励引起的随机振动。     

Field intensity factors around inclusion corners in 0–3 and 1–3 composites subjected to thermo-mechanical loads

A super inclusion corner apex element for polygonal inclusions in 0–3 and 1–3 composites is developed by using numerical stress and displacement field solutions based on an ad hoc finite element eigenanalysis method. Singular stresses near the apex of inclusion corner under thermo-mechanical loads can be obtained by using a super inclusion corner apex element in conjunction with hybrid-stress elements. The validity and the applicability of this technique are established by comparing the present numerical results with the existing solutions and the conventional finite element solutions. As examples of applications, a square array of square inclusions in 0–3 composites and a rectangular array of rectangular inclusions in 1–3 composites are considered. All numerical examples show that the present numerical method yields satisfactory solutions with fewer elements and is applicable to complex problems such as multiple singular points or fields in composite materials.     

NUMERICAL GRID GENERATION OF AN IRREGULAR REGION

A procedure of numerical conformal mapping is established to generate grids of a two-dimensional irregular region for further computations. The approach employs a sequence of Zⁿ transformations to map an irregular region into a quadrilateral region with right angles at each of the four corners. This quadrilateral region is then transformed into a rectangular domain by using the boundary integral element method to solve the Laplace mapping equations. Grids are generated in the transformed rectangular domain and are mapped inversely into the original irregular region. The present technique of grid generation is demonstrated and verified in two benchmark problems. For physical applications, steady-state temperature distributions in a circle and an area bounded by two triangles are calculated and verified, using the present techniques. The present technique of numerical conformal mapping can generate grids for the finite element method or boundary-fitted co-ordinates for the finite difference method. © 1997 by John Wiley & Sons, Ltd.     

Fundamental solution for a layered porous half space subject to a vertical point force or a point fluid source

The focus of this contribution is to develop a transmission and reflection matrices (TRM) method for a layered porous half-space subject to a point force or a fluid point source. Applying the Hankel and the Fourier transformation, the general solutions for the displacements, stresses and pore pressure are derived from the potentials for the solid skeleton and the pore fluid as well as the governing equations of Biots theory. The transmission and reflection matrices (TRM) for each interface are obtained by using the general solutions as well as the continuity conditions at the interface. The TRM method for the layered porous medium is developed on the basis of the transmission and reflection matrices (TRM) and the boundary conditions as well as the source terms for the point force or the fluid point source. The fundamental solutions of the point force and the point fluid source in both the frequency domain and the time domain are obtained by using the proposed TRM method. Some numerical examples are given in the paper.     

基于波叠加方法的水下声源辐射声场预报及实验研究

根据基于波叠加方法的声全息技术研究了水下声源的辐射声场预报问题,通过水听器阵列测得的复声压预报三维空间声场的声特性。数值仿真分析了一有限长圆柱壳模型在不同频率力激励作用下的声场预报精度,发现测量阵列尺寸与结构尺寸相近即可准确预测声场。水池和湖上实验分别对柱形换能器声源和加肋双层圆柱壳受激辐射声场进行了预测并和实测值进行了对比,结果表明该方法是一种稳健有效的声场预报方法。不同频率下,二者误差一般在3dB以内,能够满足工程需要。为实际水下大型结构的空间声场预报和降噪性能预估提供了工程参考。     

Calculation of the average solid angle subtended by a detector to source in a parallel plane by a Monte Carlo method

A short computer program is described for a PC which uses a Monte Carlo method to calculate the average solid angle subtended by a rectangular or circular detector window to a coaxial or non-coaxial rectangular, circular or point source. The advantage of the Monte Carlo method is that it allows the calculation of average solid angle for source-detector geometries that are difficult to analyse by analytical methods. The values of solid angle are calculated to accuracies of typically better than 0.1%. The calculated values from the Monte Carlo method agree closely with those produced by polygon approximation and numerical integration by Gardner and Verghese, and others.     

随机参数梁在考虑热弹耦合下的动力响应分析

以随机参数梁为研究对象,分析其在温度载荷和力载荷共同作用并考虑热弹耦合关系时的动力响应。建立了热弹耦合动力学有限元模型,给出了在时间域内差分离散、相互交替迭代的耦合计算方法。利用随机因子法推导了结构温度场和动力响应的数字特征表达式,其中温度场的求解利用θ 时间积分法,动力响应则利用Newmark-β 积分法。在求出结构各时间步温度场和动力响应数字特征的基础上,应用耦合算法获得了整个时间域内的结构响应数字特征。通过悬臂梁算例分析了热弹耦合项对动力响应的影响,并考察了诸随机参数分散性对结构动力响应分散性的影响。     

Reconstruction of a time-dependent source term in a time-fractional diffusion equation

This paper is devoted to determine a time-dependent source term in a time-fractional diffusion equation by using the usual initial and boundary data and an additional measurement data at an inner point. Based on the separation of variables and Duhamel's principle, we transform the inverse source problem into a first kind Volterra integral equation with the source term as the unknown function and then show the ill-posedness of the problem. Further, we use a boundary element method combined with a generalized Tikhonov regularization to solve the Volterra integral equation of the fist kind. The generalized cross-validation choice rule is applied to find a suitable regularization parameter. Four numerical examples are provided to show the effectiveness and robustness of the proposed method.     

基于滞变阻尼模型的时域计算方法

复阻尼时域运动方程的自由振动解中包含发散项,导致时域数值计算结果不能稳定收敛。在复阻尼模型的频域运动方程基础上可得到滞变阻尼模型的时域运动方程。针对滞变阻尼模型的特点,依据复平面法和地震加速度的三角级数表达式,该文提出了滞变阻尼模型的时域理论计算方法;假定时间步长内结构的振动响应为简谐振动响应,同时借助于常平均加速度法,提出了滞变阻尼模型的时域数值计算方法。算例分析表明,与复阻尼模型的时域数值计算方法相比,滞变阻尼模型的时域理论计算方法和时域数值计算方法可有效避免时域发散现象;滞变阻尼模型的时域理论计算结果和时域数值计算结果与复阻尼模型的频域计算结果近似相等,进一步证明了该文方法的正确性。     

A gradient smoothing method (GSM) with directional correction for solid mechanics problems

A novel gradient smoothing method (GSM) is proposed in this paper, in which a gradient smoothing together with a directional derivative technique is adopted to develop the first- and second-order derivative approximations for a node of interest by systematically computing weights for a set of field nodes surrounding. A simple collocation procedure is then applied to the governing strong-from of system equations at each node scattered in the problem domain using the approximated derivatives. In contrast with the conventional finite difference and generalized finite difference methods with topological restrictions, the GSM can be easily applied to arbitrarily irregular meshes for complex geometry. Several numerical examples are presented to demonstrate the computational accuracy and stability of the GSM for solid mechanics problems with regular and irregular nodes. The GSM is examined in detail by comparison with other established numerical approaches such as the finite element method, producing convincing results.     

无限地基相互作用力时域求解的阻尼溶剂逐步抽取法

无限地基相互作用力时域求解的精度及效率是面向实际工程结构动力分析的关键问题。基于阻尼抽取法模拟地基无限域动力特性的思想,从数值实现中的误差源出发,提出了一种施加较大附加人工阻尼再分步依次移频抽取的阻尼溶剂逐步抽取法,并给出了具体实现公式。该方法可以最大限度地消除反射波波动能量及抽取人工高阻尼的影响,提高了算法的精度,降低了人工高阻尼与地基区域大小的相互制约性,并能适应地基有限区域表面几何结构复杂多变的情况,具有较高的工程实用价值。最后,通过对典型三维半无限空间问题的动力反应分析,将计算结果与精确解,阻尼抽取法模型和粘弹性人工边界模型进行对比研究,证明了该方法具有良好的精度和计算效率,并对不规则地基有限域模型进行分析,验证其良好的工程适用性。