脉冲风洞短时测力信号的延拓与动态载荷辨识方法

研究了一种可快速辨识脉冲风洞中试验模型所受动态载荷的方法。给出了载荷、系统单位脉冲响应函数、天平输出三者的时域离散化模型,指出后者是前两者线性卷积的截断;将天平短时振荡输出延拓为完整的线性卷积结果,对前两者补零延拓,将上述模型转化为圆周卷积形式,进而通过离散傅里叶变换得到三者的频域离散化模型,求解频域模型得到载荷。通过单自由度系统简单载荷、多自由度系统复杂载荷两个数值模拟算例验证了该方法仅需对测量信号低通滤波即可准确辨识出载荷;经风洞试验,验证了方法的准确性和实用性。     

时域工况传递路径分析方法

针对非稳态工况振动噪声的传递路径分析需求,将频域工况传递路径分析方法推广到时域,利用指示点和目标点的时域工况数据实现路径分解,提出了时域工况传递路径分析方法。利用时域传递率函数建立了目标点与指示点时域工况数据的卷积关系,并将其离散化后以矩阵方程的形式表示,然后采用Tikhonov正则化求解,即可利用不同工况下目标点和指示点的时域响应数据计算出时域传递率函数,能进行振动噪声的分解和预测。通过九自由度集中质量块模型仿真与简易车身骨架模型试验进行检验,结果表明所提出的方法具有较好的精度,可以准确地进行时域传递路径分析,并能准确预测目标点在非稳态工况下的响应。     

应用Gurtin变分原理计算动力响应的单步时间元法

本文以Ｇｕｒｔｉｎ变分原理为基础，采用三次Ｈｅｒｍｉｔｅ插值函数对时间域进行离散，提出了一种计算动力学初值问题的单步时间元法，并构造出相应的无条件稳定计算格式。应用表明，本文方法比现有动力分析方法具有更高的数值精度。     

一种基于离散变分原理的非线性动力系统参数识别方法

提出了一种辨识非线性动力系统模型参数的方法。首先将待辨识参数的导数引入到系统输出误差代价函数中;然后利用离散变分原理导出关于待辨识参数的差分方程,并与系统方程一同求解;最后通过迭代运算使待辨识参数从给定的初值收敛到稳定真值。利用本方法对线性和非线性振动系统的模型参数分别进行了参数识别仿真,数值计算结果证明了方法的有效性。     

受偏压作用薄壁结构的稳定分析

本文提出了一种基于势能原理的薄壁杆件稳定分析的半离散方法，采用转换Ｂ３样条函烤作为横截面纵向位移的插值函数通过变分原理，导出控制微分方程及自然边界条件，利用常微分方程求解器求解。     

数值流形方法的数学推导及其应用

以往的数值流形方法都是以最小势能原理或变分原理为基础来建立求解方程的。但在实际工程中科技人员所遇到的有些实际问题,其控制方程所对应的泛函往往是难以找到的,在这些情况下就无法应用变分方法来建立数值流形方法的求解方程,而必须寻找较为一般的方法来推导数值流形方法的求解方程。因此,研究了如何从加权残数法出发建立数值流形方法的求解方程。在此过程中,通过建立弹性力学方程的数值流形方法,可以看出,通过选取适当的权函数,该方法最终的求解方程将转化为以最小势能原理或以变分原理为基础的离散形式。为了说明方法的有效性,求解了岩石试件中含单裂隙双边受拉的问题,并给出了裂隙尖端的应力强度因子和应力场的变化关系。     

粘弹性薄板的热振动

首先从热粘弹性材料的各向同性本构方程出发,利用Laplace变换方法,引入薄板的“结构函数”与“热函数”,建立了薄板热振动的数学模型。然后,采用近代卷积双线性形式和传统笛卡儿双线性形式找到了相应的简化Gurtin型变分原理。最后,利用Ritz法和Laplace变换技术,考察热载对粘弹性薄板响应的影响。     

LTI系统中零状态响应两种时域解法的难点与研究

零状态响应是电子技术相关理论课程中的一个重要概念,通过对卷积法和经典法求解线性时不变(LTI)系统零状态响应的叙述,着重讨论卷积法中求冲激函数的一种便捷方法算子法和经典法求特解时一般文献中没有涉及的一种情况的分析,起到对相关理论进行完善的作用.首先概述每种方法的基本求解原理,然后通过实例说明具体求解中的难点,易错点.有助于我们加深对两种时域系统分析方法的理解与掌握,也对本课程教师讲解时域中零状态相应求解具有一定的参考价值.     

基于三场变分原理的对偶mortar有限元法

通过引入独立媒介面，将mortar有限元法由二场变分原理推广到三场变分原理。通过采用满足双正交性条件的对偶基函数离散Lagrange乘子空间，实现了Lagrange乘子的凝聚，由此提出了基于三场变分原理的对偶mortar有限元法。提出的新方法同时解决了常规mortar元的约束交叉、主从偏见及求解效率等问题。自主编制了相应的计算程序，并采用两个三维数值算例对新方法进行了验证。研究结果表明:基于三场变分原理的对偶mortar方法对界面连续性条件的求解精度高，可有效用于含约束交叉的非协调网格计算，所支持的复杂子区域划分使得有限元分析更为灵活。     

一维动边界问题的一种变分解法及应用

本文从可运边界变分原理出发，讨论了一模型问题，即一维弹塑性扭转问题在引区间映射后分时产生的矛盾，并给出了正确的变分列式，同时为进一步认识用可动边界变分原理求解弹塑性问题的性质，我们用线性有限元求解一维问题，给出了解的分布及收敛情况。     

Space-Time Adaptive Fup Multi-Resolution Approach for Boundary-Initial Value Problems

The space-time Adaptive Fup Collocation Method (AFCM) for solving boundary-initial value problems is presented. To solve the one-dimensional initial boundary value problem, we convert the problem into a two-dimensional boundary value problem. This quasi-boundary value problem is then solved simultaneously in the space-time domain with a collocation technique and by using atomic Fup basis functions. The proposed method is a generally meshless methodology because it requires only the addition of collocation points and basis functions over the domain, instead of the classical domain discretization and numerical integration. The grid is adapted progressively by setting the threshold as a direct measure of the solution accuracy at a given resolution level. At higher resolution levels, collocation points are only added in the space-time sub-domains where the solution correction is greater than the prescribed threshold. In contrast to the classical time-stepping schemes, in which globally accumulated errors can arise and which are not easily adapted to multiple time steps, the space-time AFCM covers all space and time multiple scales, while global error is strictly controlled in time by an a priori threshold.     

基于逆向滤波器的动态载荷时域识别方法

动态载荷的时域识别方法由于涉及到载荷与响应的复杂卷积关系，是难度较高的复杂的反分析问题。目前针对离散系统的方法都是建立递推连锁计算格式来进行的，递推连锁计算格式的缺点是对初值敏感和误差累积。本文建立了基于结构动力问题的逆向滤波器的计算格式，从根本上解决了初值敏感和误差累积问题，从而提高了数值计算稳定性和动态载荷识别精度。由于使反分析过程转化为类似正分析过程，使文中提出的方法有应用方便、计算效率高的特点，并为动态载荷的实时识别技术建立了理论基础。     

Shape optimization using time evolution equations

In this study, we deal with a numerical solution based on time evolution equations to solve the optimization problem for finding the shape that minimizes the objective function under given constraints. The design variables of the shape optimization problem are defined on a given original domain on which the boundary value problems of partial differential equations are defined. The variations of the domain are obtained by the time integration of the solution to derive the time evolution equations defined in the original domain. The shape gradient with respect to the domain variations are given as the Neumann boundary condition defined on the original domain boundary. When the constraints are satisfied, the decreasing property of the objective function is guaranteed by the proposed method. Furthermore, the proposed method is used to minimize the heat resistance under a total volume constraint and to solve the minimization problem of mean compliance under a total volume constraint.     

Analytical time integration for BEM axisymmetric acoustic modelling

In this work, a numerical time‐domain approach to model acoustic wave propagation in axisymmetric bodies is developed. The acoustic medium is modelled by the boundary element method (BEM), whose time convolution integrals are evaluated analytically, employing the concept of finite part integrals. All singularities for space integration, present in the expressions generated by time integration, are treated adequately. Some applications are presented to demonstrate the validity of the analytical expressions generated for the BEM, and the results obtained with the present approach are compared with those generated by applying numerical time integration. Copyright © 2007 John Wiley & Sons, Ltd.     

A symmetric Galerkin boundary element method for 3d linear poroelasticity

In this paper, a symmetric Galerkin boundary element formulation for 3D linear poroelasticity is presented. By means of the convolution quadrature method, the time domain problem is decoupled into a set of Laplace domain problems. Regularizing their kernel functions via integration by parts, it is possible to compute all operators for rather general discretizations, only requiring the evaluation of weakly singular integrals. At the end, some numerical results are presented and compared with a collocation BEM. Throughout these studies, the symmetric Galerkin BEM performs better than the collocation method, especially for not optimal discretizations parameters, i.e. a bad relation of mesh to time-step size. The most obvious advantages can be observed in the fluid flux results. However, these advantages are obtained at a higher numerical cost.     

A fast multi‐level convolution boundary element method for transient diffusion problems

A new algorithm is developed to evaluate the time convolution integrals that are associated with boundary element methods (BEM) for transient diffusion. This approach, which is based upon the multi‐level multi‐integration concepts of Brandt and Lubrecht, provides a fast, accurate and memory efficient time domain method for this entire class of problems. Conventional BEM approaches result in operation counts of order O(N²) for the discrete time convolution over N time steps. Here we focus on the formulation for linear problems of transient heat diffusion and demonstrate reduced computational complexity to order O(N^3/2) for three two‐dimensional model problems using the multi‐level convolution BEM. Memory requirements are also significantly reduced, while maintaining the same level of accuracy as the conventional time domain BEM approach. Copyright © 2005 John Wiley & Sons, Ltd.     

无限地基-结构动力相互作用分析的分区递归时域算法研究

基于阻尼抽取法,针对结构-无限地基动力相互作用时域分析提出了一种新的分区递归数值求解算法,包括逐步积分形式的地基作用力计算公式及动力相互作用分析中,基于子结构法的具体数值实现过程。该算法隐式地满足了无限介质辐射条件,可方便地确定地基作用力与交界面位置变位的关系,消除了无限地基动刚度时域算法中的频率相关性及褶积分,此外,时域子结构方式的求解可以方便地考虑结构部分的非线性力学特征。以实例的形式说明了该方法良好的精度与应用的简便性。     

Design problem of the profile or the cascade of profiles and construction of orthogonal networks using the Riemann surfaces for the multiform singularities

The complex potential induced by the source-vortex distribution is a multi-values function. In order to treat the field problem defined by the Dirichlet type boundary condition, it is necessary to get its correct value which has to be taken from an appropriate sheet of the Riemann surface. For the analytical formulations of a homogeneous density distribution over a segment or a cascade of segments, it can be done that the multi-value part is located at one of the end points of each segment. An algorithm is proposed to get the appropriate definition according to the relative positions of the induction element with the reception point. The construction of an orthogonal network inside a domain by solving the Dirichlet problem is shown. The simple layer distributions on the boundaries of the domain are used to generate the field in this example. The turbomachine blading design in connection with the flow field problem is described. The proposed method admits the thickness distribution and the bound vortex distribution as the initial data. In the case of the 2D cascade, we show how to define the boundary conditions in order to obtain a properly posed field problem.     

基于最小转换能原理的一种逐步积分法

基于Benthien_Gurtin 给出的拉普拉斯空间上相应的最小转换能原理,将拉普拉斯空间上的泛函恢复到原空间后给出一个只含单重卷积形式的泛函。对此泛函相继进行空间和时间域离散分别给出了新的泛函。采用含非时间步参数的三次Hermite 插值函数逼近节点位移,给出了一种用于动力响应分析的无条件稳定逐步积分算法。通过对算法的稳定性研究,选取了参数的合适值。精度分析和数值算例表明提出的方法是一种可以应用于工程实际并具有较高精度的方法。     

Initial conditions contribution in a BEM formulation based on the convolution quadrature method

This work presents a two‐dimensional boundary element method (BEM) formulation for the analysis of scalar wave propagation problems. The formulation is based on the so‐called convolution quadrature method (CQM) by means of which the convolution integral, presented in time‐domain BEM formulations, is numerically substituted by a quadrature formula, whose weights are computed using the Laplace transform of the fundamental solution and a linear multistep method. This BEM formulation was initially developed for scalar wave propagation problems with null initial conditions. In order to overcome this limitation, this work presents a general procedure that enables one to take into account non‐homogeneous initial conditions, after replacing the initial conditions by equivalent pseudo‐forces. The numerical results included in this work show the accuracy of the proposed BEM formulation and its applicability to such kind of analysis. Copyright © 2006 John Wiley & Sons, Ltd.