模态应变能方法精确性和适用性研究

介绍了非比例阻尼体系动力分析的模态应变能方法和状态方程法,在频域内和时域内分析比较了具有Maxwell阻尼的多自由度模型响应的精确解和近似解,并据此分析了模态应变能方法的精确性和适用性,数值算例结果表明:在一定条件下模态应变能方法具有较高的精确性,同时在工程应用方面该方法也具有较好的适用性。     

Modelling the transient interaction of a thin elastic shell with an exterior acoustic field

Coupled finite and boundary element methods for solving transient fluid–structure interaction problems are developed. The finite element method is used to model the radiating structure, and the boundary element method (BEM) is used to determine the resulting acoustic field. The well‐known stability problems of time domain BEMs are avoided by using a Burton–Miller‐type integral equation. The stability, accuracy and efficiency of two alternative solution methods are compared using an exact solution for the case of a thin spherical elastic shell. The convergence properties of the preferred solution method are then investigated more thoroughly. Copyright © 2007 John Wiley & Sons, Ltd.     

用LES和无限元耦合方法预报潜艇流噪声

为了系统地研究潜艇流噪声的特点,采用大涡模拟(LES)与声学无限元方法耦合,对潜艇进行频域噪声数值预报。在潜艇水动力性能及压力分布的计算后,再与试验结果对比分析,验证了水动力计算方案的准确性。在此基础上,结合声学无限元方法,对潜艇流噪声进行数值模拟,并对特征点进行频域分析。经噪声分布云图和远场特征点频谱曲线的详细分析后,可发现随着频率增加,辐射区间均会增多,而相同频率下四极子噪声辐射区间要多于偶极子。相比于面声源,体声源在总声级中的贡献度较小,可以忽略不计。由于计算的特征点总声压级与文献所提供结果吻合,验证了所采用噪声预报方法的准确性。     

A frequency domain model for generating B-mode images with array transducers

A frequency domain B-mode imaging model applicable to linear and phased array transducers was developed for simulating ultrasound images of random media. Computations are based on an approximation that is less restrictive than the Fresnel approximation. The model is compared with the exact time domain impulse response method, regarded as the "gold standard". In a typical application, errors in simulated rf waveforms are less than 1% regardless of the steering angle for distances greater than 2 cm, yet computation times are on the order of 1/150 of those using the exact method. This model takes into account the effects of frequency-dependent attenuation, backscattering, and dispersion. Modern beam-forming techniques such as apodization, dynamic aperture, elevational focusing, multiple transmit focusing and dynamic receiving focusing also can be simulated.     

Discrete equivalent time integration methods for transient analysis

It was recently shown in a series of papers that the frequency response of temporally discretized finite element equations and, consequently, the achievable accuracy cannot be manipulated independently in different frequency ranges. In addition, there exist limitations on the achievable accuracy of a time integration method no matter what the order of accuracy of the method is. Motivated by this fact, a family of time integration methods is derived in the time domain based on the principle that the exact solution of the semidiscrete equation of a system and the solution of the time integration method match at discrete time steps. It is necessary to pursue an exact match at discrete time steps, i.e. discrete equivalence, since the solutions of semidiscrete equations are obtained only at the time steps. Two time integration methods, that are exact at the time steps, are obtained based on the impulse and ramp response invariance principles. Numerical examples are presented to show the advantage of the proposed methods and to compare the performance of them with the performance of some popular methods. Copyright © 2003 John Wiley & Sons, Ltd.     

基于频域互相关的LED晶粒阵列快速视觉检测

为了满足LED晶粒视觉检测的实时性要求,提出了一种频域互相关的快速模板匹配方法。首先通过一种递推求和算法将LED晶粒阵列图像的灰度在空间域进行归一化处理,然后利用快速傅里叶变换到频率域进行模板与LED晶粒阵列图像的互相关运算,快速定位所有LED晶粒的像素坐标。对于清晰的二值晶粒图像,可以省去归一化处理,检测效率更高。实验结果表明:对于复杂结构的LED晶粒,检测效率远高于传统的NCC模板匹配,比常用的序贯相似检测（SSDA）算法效率提高1倍以上。该方法能够用于各种LED分选或固晶系统中的晶粒检测。     

Earthquake response analysis in the time domain for 2D soil–structure systems using analytical frequency‐dependent infinite elements

This paper presents a time domain method for soil–structure interaction analysis under seismic excitations. It is based on the finite element formulation incorporating analytical frequency‐dependent infinite elements for the far‐field soil region. Equivalent earthquake input forces are calculated based on the free‐field responses along the interface between the near‐ and far‐field soil regions using the fixed exterior boundary method in the frequency domain. Then, the input forces are transformed into the time domain by using inverse Fourier transform. The dynamic stiffness matrices of the far‐field soil region formulated using the analytical frequency‐dependent infinite elements in the frequency domain can be easily transformed into the corresponding matrices in the time domain. Hence, the response can be analytically computed in the time domain. A recursive procedure is proposed to compute the interaction forces along the interface and the responses of the soil–structure system in the time domain. Earthquake response analyses have been carried out on a multi‐layered half‐space and a tunnel embedded in a layered half‐space, and results are compared with those obtained by the conventional method in the frequency domain. Copyright © 2003 John Wiley & Sons, Ltd.     

Precorrected FFT accelerated BEM for large‐scale transient elastodynamic analysis using frequency‐domain approach

A precorrected fast Fourier transform (pFFT) accelerated boundary element method (BEM) for large‐scale transient elastodynamic analysis is developed and described in this paper. The frequency‐domain approach is used. To overcome the ‘wrap‐around’ problem associated with the discrete Fourier transform, the exponential window method (EWM) is employed and incorporated in the frequency‐domain BEM. An improved implementation scheme of the pFFT method based on polynomial interpolation technique is developed and applied to accelerate the elastodynamic BEM. This new scheme reduces the memory required to save the convolution matrix by a factor of 8. To further improve the efficiency of the code, a newly developed linear system solver based on the induced dimension reduction method is employed. Its performance is investigated and compared with that of the well‐known GMRES. The accuracy and computational efficiency of the method are evaluated and demonstrated by three examples: a classical benchmark, a plate subject to an impact loading and a porous cube with nearly half million DOFs subject to a step traction loading. Both analytical and experimental results are employed to validate the method. It has been found that the EWM can effectively resolve the wrap‐around problem and accurate time responses for an arbitrarily chosen time period can be obtained. Copyright © 2011 John Wiley & Sons, Ltd.     

Accurate radiation boundary conditions for the time‐dependent wave equation on unbounded domains

Asymptotic and exact local radiation boundary conditions (RBC) for the scalar time‐dependent wave equation, first derived by Hagstrom and Hariharan, are reformulated as an auxiliary Cauchy problem for each radial harmonic on a spherical boundary. The reformulation is based on the hierarchy of local boundary operators used by Bayliss and Turkel which satisfy truncations of an asymptotic expansion for each radial harmonic. The residuals of the local operators are determined from the solution of parallel systems of linear first‐order temporal equations. A decomposition into orthogonal transverse modes on the spherical boundary is used so that the residual functions may be computed efficiently and concurrently without altering the local character of the finite element equations. Since the auxiliary functions are based on residuals of an asymptotic expansion, the proposed method has the ability to vary separately the radial and transverse modal orders of the RBC. With the number of equations in the auxiliary Cauchy problem equal to the transverse mode number, this reformulation is exact. In this form, the equivalence with the closely related non‐reflecting boundary condition of Grote and Keller is shown. If fewer equations are used, then the boundary conditions form high‐order accurate asymptotic approximations to the exact condition, with corresponding reduction in work and memory. Numerical studies are performed to assess the accuracy and convergence properties of the exact and asymptotic versions of the RBC. The results demonstrate that the asymptotic formulation has dramatically improved accuracy for time domain simulations compared to standard boundary treatments and improved efficiency over the exact condition. Copyright © 2000 John Wiley & Sons, Ltd.     

基于香农采样定理的结构风振时域计算改进

基于同步测点的风压时程数据的响应计算有两种方法:时域法和频域法,它们得到的结果存在一定的差异。针对如何改善时域算法的精度进行研究,提出基于香农采样定理对风压时程数据进行加密的方法。将此方法运用到一个有解析解的两自由度结构算例和一个实际工程算例中,对采样数据量和采样频率都一定的荷载时程数据进行香农插值加密;分别采用插值加密之后的数据与未插值加密的数据进行计算,得到频域和时域结果。通过计算结果的比较得到以下结论:荷载时程数据相同的情况下,对于风致振动响应,频域计算的结果一般比时域计算更精确,时域计算的误差主要由高频部分的误差引起;运用香农采样定理,对已采得的数据进行插值加密,频域计算精度基本不变,但时域计算精度能得到提高。     

AN EXACT METHOD FOR ANALYSING ELASTODYNAMIC RESPONSE OF ANISOTROPIC LAMINATES TO LINE LOADS

SUMMARY

An exact matrix formulation for analysing the responses of anisotropic laminated plates subjected to line loads is presented. In this formulation, a Fourier transform with respect to the horizontal spatial co-ordinate is employed and wave modes for a layer are obtained from an eigenvalue equation. Displacements in the wavenumber domain are obtained by using boundary conditions. A complex path is used and a new adaptive quadrature scheme is proposed to evaluate the inverse Fourier integration to obtain the displacement in the frequency domain. An exponential window method is used to compute responses in the time domain. Complex paths are investigated in detail to improve the efficiency for computing the responses of the plates for both pure and viscoelastic materials in both time and frequency domains. Numerical examples are presented to illustrate the present method.     

Efficiency and accuracy in simulation of random fields

A direct method for the conditional simulation of a stationary, Gaussian scalar random field is compared with an alternative formulation which uses frequency domain probability density functions. In both cases the random field is described by given correlation or spectral density functions, and no restrictions are placed on these functions, except that they must be positive definite. Efficient implementation techniques are investigated for both general methods. The major computational effort in the most efficient implementations of both procedures is in the solution of linear algebraic equations in which the coefficients are spectral densities. The direct method is shown to be significantly more efficient than existing methods for applying the probability density function technique. However, a new implementation method for the latter technique is also presented, and it equals the efficiency of the direct method. Problems of numerical accuracy due to ill-conditioned matrices are shown not to be severe except when using an inherently problematic form for the spectral density. Numerical examples demonstrate that either method can simulate highly coherent time histories.     

基于频域法的深水钻井隔水管波激疲劳分析

Wave-loading fatigue failure is one of main failure modes of deepwater drilling riser. Wave-loading fatigue analysis of riser provides guidance for fatigue design and management of riser in order to increase its service life. Methods for analyzing wave induced vibration and fatigue were established in frequency domain. Solver for riser fatigue calculation was developed based on MATLAB software. Wave-loading fatigue of the riser system in the South China Sea was calculated in frequency domain and compared with calculated fatigue based on time domain method. The results show that dynamic analysis of riser in frequency domain reaches convergence after several iteration steps. Compared with time domain method, frequency domain method enhances computation efficiency greatly. The response of riser system is a wide-band process so rainflow correction coefficient should be used in calculating riser fatigue. The wave-loading fatigue damage of riser in frequency domain is almost same with that in time domain. Riser fatigue analysis method proposed in this paper can be used for inertial fatigue analysis.     

Application of Schwarz-Christoffel Mapping to Permanent-Magnet Linear Motor Analysis

Several well-known analytical techniques exist for the force profile analysis of permanent-magnet linear synchronous motors. These techniques, however, make significant simplifications in order to obtain the magnetic field distribution in the air gap. From the field distribution, the force profile can be found. These widely used techniques provide a reasonable approximation for force profile analysis, but fail to give really accurate results in the sense of the exact shape of the force profile caused by effects that due to simplification are not fully included. To obtain the exact shape for the force profile in these cases, the computationally expensive finite-element method (FEM) is often applied. In this paper, an elegant semianalytical approach is presented to acquire the force profile. First, the magnetic field distribution in the air gap is determined by means of Schwarz-Christoffel (SC) mapping. The SC mapping allows a slotted structure of the machine to be mapped to a geometrically simpler domain for which analytic solutions are available. Subsequently, the field solution in the slotted structure can be determined by applying the mapping function to the field distribution in the simplified domain. From the resulting field distribution, the force profile is calculated by means of the Maxwell stress tensor. The results are compared with those from the commonly used equivalent magnetic circuit modeling and 2-D FEM software to demonstrate the accuracy which can be reached by application of the SC method.     

光滑有限元的声学研究：时域和频域分析

摘　要：在使用有限元进行声场的数值模拟中,存在着两个主要误差,一个是数值方法中常规的插值误差,另外一个是计算声学中所特有的耗散误差(dispersion error),后者则是影响声学模拟仿真置信度的最重要因素。产生耗散误差的本质原因是由于有限元的数值模型刚度“偏硬”造成的。为了控制耗散误差,最重要的是使数值模型更好的反映真实模型。本文采用了一种基于边光滑的有限元方法(ES-FEM)来对声场的时域和频域进行数值模拟研究。该方法只采用对复杂问题域适应性很强的三角形网格,通过引进基于边的广义梯度光滑技术,能够使得有限元系统得到适当的“软化”。关于时域和频域的算例表明了在使用同样网格的情况下,本方法在声学模拟中的精度都要比有限元模型的高。     

自适应时延估计在蛙人超短基线定位中的应用

蛙人超短基线(Ultra-Short Base Line, USBL)定位设备实现浅水环境下高精度定位的关键技术之一是精确的时延估计。由于自适应时延估计方法具备环境自适应能力强的特点,文章将混合调制的拉格朗日直接时延估计方法应用于蛙人USBL定位时的高精度测向上,它可以在信标信号中心频率已知的情况下将小数时延滤波器调制到信号中心频率处,以较低的阶数提供更高的时延估计精度;并根据USBL阵型和信号自身的特点,对混合调制的拉格朗日直接时延估计在低信噪比下的具体使用模式进行了探讨和仿真验证;结果显示,所采用的自适应时延估计方法可以在中低信噪比下提供1°～3°的定位测向精度。     

Localized meshless point collocation method for time-dependent magnetohydrodynamics flow through pipes under a variety of wall conductivity conditions

In this article a numerical solution of the time dependent, coupled system equations of magnetohydrodynamics (MHD) flow is obtained, using the strong-form local meshless point collocation (LMPC) method. The approximation of the field variables is obtained with the moving least squares (MLS) approximation. Regular and irregular nodal distributions are used. Thus, a numerical solver is developed for the unsteady coupled MHD problems, using the collocation formulation, for regular and irregular cross sections, as are the rectangular, triangular and circular. Arbitrary wall conductivity conditions are applied when a uniform magnetic field is imposed at characteristic directions relative to the flow one. Velocity and induced magnetic field across the section have been evaluated at various time intervals for several Hartmann numbers (up to 10⁵) and wall conductivities. The numerical results of the strong-form MPC method are compared with those obtained using two weak-form meshless methods, that is, the local boundary integral equation (LBIE) meshless method and the meshless local Petrov–Galerkin (MLPG) method, and with the analytical solutions, where they are available. Furthermore, the accuracy of the method is assessed in terms of the error norms L ₂ and L _∞, the number of nodes in the domain of influence and the time step length depicting the convergence rate of the method. Run time results are also presented demonstrating the efficiency and the applicability of the method for real world problems.     

基于快速多极子边界元法的齿轮箱声场分析

齿轮箱是广泛应用的工程机械零部件,准确地模拟其辐射声场对后续的降噪优化设计有着重要作用。边界元方法非常适合分析此类无限域下的声辐射问题。但传统边界元方法有着计算效率低、内存占用高的缺点。该研究发展了宽频的快速多极子边界元方法,并运用该方法计算了齿轮箱在特定频率下的场点声压以及辐射声场。通过对比商用软件的分析结果,验证了所提快速边界元方法的准确性。此外,运用多核并行计算方法,对计算量较大的扫频分析进行加速计算,最终快速、准确地获取了齿轮箱辐射声场的扫频结果。     

A PDF discretization scheme in wavenumber–frequency joint spectrum for simulating multivariate random fluctuating wind fields

The wavenumber–frequency joint spectrum-based spectral representation method is an effective method for simulating multivariate random fluctuating wind fields. However, the simulation efficiency may not be quite satisfactory when the uniform discretizations in both frequency and wavenumber domains are employed. In this paper, a probability density function discretization scheme in wavenumber domain, which is actually an uneven discretization scheme, is proposed to alleviate the computational burden. In the proposed scheme, the wavenumber–frequency joint spectrum at a characteristic frequency is first taken as a probability density function. Then, the wavenumber domain is unevenly discretized according to the probability density function. Since the wavenumber–frequency joint spectrum may decay very fast in wavenumber domain, a uniform discretization is further applied in large intervals in wavenumber domain. Finally, the unevenly discrete wavenumbers and wavenumber intervals are substituted into the wavenumber–frequency joint spectrum-based spectral representation method for generating samples of multivariate random fluctuating wind fields, where the frequency domain is still uniformly discretized. The accuracy and efficiency of the proposed discretization scheme are compared with the uniform and conventional uneven discretization schemes. Practical applications of the proposed method are also investigated in various engineering scenarios.     

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。