线性阻尼杆振动问题基于变量变换的多辛算法

提出线性阻尼杆振动问题基于变量变换的多辛离散算法。首先通过变量变换把耗散系统化为保守系统。其次以变换变量组成状态向量并采用中点离散方法构造中点Box多辛离散格式,然后,基于空间层的状态变量建立矩阵形式的递推关系,最后结合空间边界条件和初始条件建立线性方程组求解。研究结果表明,构造的多辛算法不仅能够保持系统守恒型几何性质,通过状态变量合理表示了边界条件,而且能够较准确地体现系统的耗散效应。     

基于卷积型原理的时空样条元

结构动力分析是工程设计中的重要组成部分,传统动力分析不能全面反映动力初值特征,而Gurtin变分原理则被认为是目前唯一能全面反映动力初值特征的变分原理.本文以Gurtin变分原理为基础,空间和时间上同时采用样条元,建立了计算梁的动力初值问题的样条元法。算例表明, 与现有的分析方法相比,本文具有更高的精度。     

基于简化Gurtin型变分原理的平面问题动力响应分析

本文首先建立有阻尼线弹性动力学一类变量的简化Ｇｕｒｔｉｎ型变分原理,它能反映动力学初值一边值问题的全部特性。然后,以该简化Ｇｕｒｔｉｎ型变分原理为基础,提出时间域采用五次及七次一般Ｈｅｒｍｉｔｅ插值多项式插值的时间子域法和空间域采用有限元法相结合的新方法,进行了平面问题的动力响应分析。同时本文还给出了五次及七次Ｈｅｒｍｉｔｅ插值多而式无条件稳定的算法和算例。具体算例表明这种新方法的精度和计算效率都     

结构动力响应的可视化分析

采用状态空间迭代法来计算动力响应量，对空间域采用非线性有限元法分析计算，对时间域采用状态空间迭代法计算。同时编制了用于非线性分析的计算机仿真程序。可完成工程结构动力响应的可视化分析。     

基于均匀七次B样条插值求解动力响应的逐步积分法

为求解结构动力响应提出新的时间积分法。该方法采用均匀七次B样条插值近似对局部时间域节点位移、速度及加速度进行离散。给出动力平衡方程求解的逆推格式与算法流程。分析表明,通过选择合适参数可提高计算精度,且使算法绝对稳定。计算数值解精度较高,明显优于传统的Newmark法与Wilson-θ法。     

状态空间迭代法计算弹性地基板的动力响应问题

本文采用状态空间迭代法来计算弹性地基板的动力响应量，对空间城采用有限元计算，对时间域采用状态空间法。文中给出二个数值算例，其计算结果较满意。     

基于状态空间理论的结构动力响应解法

本文基于状态空间理论分析结构动力响应问题，根据结构动力学方程，引入系统的状态变量，建立状态方程，并给出了非奇次状态方程的解，对于求解矩阵指数函数有多种解法。文中着重介绍凯莱－哈密尔顿法。状态空间迭代法和精细积分法，对结构动力响应问题按三种解法分别建立了计算格式，并编制相应程序，文末给出了数值算例，其计算结果表明，状态空间法分析结构动力响应，其精度好效率高，是一种有非常有效的方法。     

网架结构动力分析的三次样条辛算法

根据对偶互补的思想,建立了网架结构动力学的相空间非传统Hamilton型变分原理。这种变分原理不仅能反映这种动力学初值-边值问题的全部特征,而且它的欧拉方程具有辛结构。基于该变分原理,空间域采用有限元法与时间子域采用三次样条函数插值的时间子域法相结合,构造了求解网架结构动力响应的一种辛算法,给出了逐步递推计算格式。数值算例结果表明,这种新方法的稳定性、计算精度和效率都明显高于Wilson-θ法和Newmark-β法。     

厚/薄板振动分析的样条无单元法

建立了厚/薄板振动分析的样条无单元法计算格式,对整个求解区域仅需少量的结点离散,无需单元分划,把挠度和剪应变作为全局的场变量,采用双向三次B样条基函数乘积的线性组合构造场函数,可以充分发挥无单元法及三次B样条基函数的优点。计算结果表明该方法适用于不同厚度,不同边界的板的动力特性分析,无剪切闭锁现象,且精度高,收敛快,未知量少,程序简便。     

流体固体动力耦合分析的有限元法

应用有限元法探讨了流体、固体接触界面由无限接触点对组成,并以接触点对的瞬态接触内力作为待定变量的流体固体动力耦合模型的数值求解方法。分析了流体、固体域插值函数的特点,用二维八节点等参元及流固接触面上的接触点对单元,对流固耦合系统进行了离散化处理;并采用变分原理推导了反映流体固体动力相互作用机理的接触约束矩阵(或称动力耦合矩阵),建立了有限元控制方程,给出了完整的数值计算方法,研编了动力耦合系统的分析程序。数值计算结果与经典理论解误差很小,验证了动力耦合模型和有限元求解方法的正确性及其较高的计算精度。     

Decentralized decoupling of multivariable control systems with unmodelled interaction

Abstract

This paper presents both state space and frequency domain approaches for the decentralized decoupling of multivariable control systems with unmodelled interaction. The controller has a configuration of two degrees of freedom. The nominal controller is tuned to satisfy the eigenvalue specification of the isolated single variable subsystem. The rejection of unmodelled coupling due to the connections or disconnections of other subsystems is controlled by the decentralized compensator. The method assumes that only local information is acquirable, no information from other subsystems and no interconnection parameters are required. This gives the convenience of single variable design for multi‐variable control applications. The decentralized compensator can also be used to improve the performance of the control system with unmodelled nonlinearity or parameter drifting. The stability of the control system with the decentralized compensator has been investigated. Two numerical examples are given to show the feasibility of the method.     

Multi‐rate digital control for a cascaded system consisting of two subsystems with different input time delays

Abstract

This paper presents a multi‐rate state‐space control scheme for digital control of a cascaded continuous‐time system with fractional time delays. First, a discrete‐time state‐space representation of a continuous‐time system with a fractional input delay is established. Based on the time‐delay digital modelling, an ideal state reconstructor is also presented such that system states are exactly reconstructed via the measurement histories of inputs and outputs without a state observer. Next, a time‐delay subsystem (designated subsystem 1) with a fast sampling rate is designed to form the inner loop of the overall system, then the designed closed‐loop subsystem 1 is cascaded with a time‐delay open‐loop subsystem 2 with a slow sampling rate. A digital modelling of the time‐delay open‐loop subsystem 2, based on a fast‐rate sampling, is also formed for obtaining the digital modelling of the overall cascaded continuous‐time system by using the block‐pulse function approximation. Then, the fast‐rate overall system is converted into a slow‐rate model via the newly developed model conversion technique. Furthermore, subsystem 2 is separated from the slow‐rate overall system via a linear transformation for achieving a reduced‐order subsystem design. As a consequence, a digital control law is determined on some specific goals for the overall system. The proposed method is suitable for digital control of a multivariable, multi‐rate, time‐delay system in which state variables are not accessible.     

Semi‐analytical analysis for multi‐directional functionally graded plates: 3‐D elasticity solutions

Semi‐analytical 3‐D elasticity solutions are presented for orthotropic multi‐directional functionally graded plates using the differential quadrature method (DQM) based on the state‐space formalism. Material properties are assumed to vary not only through the thickness but also in the in‐plane directions following an exponential law. The graded in‐plane domain is solved numerically via the DQM, while exact solutions are sought for the thickness domain using the state‐space method. Convergence studies are performed, and the present hybrid semi‐analytical method is validated by comparing numerical results with the exact solutions for a conventional unidirectional functionally graded plate. Finally, effects of material gradient indices on the displacement and stress fields of the plates are investigated and discussed. Copyright © 2009 John Wiley & Sons, Ltd.     

Spline-blended approximation of Hartmann's flow

The steady state flow problem known in magnetohydrodynamics as Hartmann's flow is converted into variational formulation and is given an approximate solution by means of the spline blended interpolation technique. The equations of motion consist of two coupled potential flow problems with homogeneous boundary conditions. The spline blended interpolation method is reduced here, because of the shape of the domain, to a cartesian product of cardinal splines with trigonometric or ordinary polynomials. ‘Exact’ boundary conditions are presented by the blending technique. The numerical results indicate that high accuracy is possible with relatively few unknowns.     

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.     

往复压缩机十字头滑块故障的小波包敏感特征提取研究

由于往复压缩机振动信号具有非平稳和低信噪比特点,利用传统的时域或频域分析方法很难提取到反应压缩机的运行状况有效特征。压缩机发生故障时,信号能量沿频率的分布与正常状态有较大差异,本文利用小波包对非平稳信号的分解和时域重构能力,提出一种基于小波包分析的多频带平均能量特征提取方法;针对各特征对故障的敏感度不同,提出了一种基于欧式距离的特征选择方法,选择的特征能较好地反映压缩机的运行状态,最后通过往复压缩机的实验数据验证了该方法的可行性和有效性。     

Exploiting semantics of temporal multi‐scale methods to optimize multi‐level mesh partitioning

Multi‐scale problems are often solved by decomposing the problem domain into multiple subdomains, solving them independently using different levels of spatial and temporal refinement, and coupling the subdomain solutions back to obtain the global solution. Most commonly, finite elements are used for spatial discretization, and finite difference time stepping is used for time integration. Given a finite element mesh for the global problem domain, the number of possible decompositions into subdomains and the possible choices for associated time steps is exponentially large, and the computational costs associated with different decompositions can vary by orders of magnitude. The problem of finding an optimal decomposition and the associated time discretization that minimizes computational costs while maintaining accuracy is nontrivial. Existing mesh partitioning tools, such as METIS, overlook the constraints posed by multi‐scale methods and lead to suboptimal partitions with a high performance penalty. We present a multi‐level mesh partitioning approach that exploits domain‐specific knowledge of multi‐scale methods to produce nearly optimal mesh partitions and associated time steps automatically. Results show that for multi‐scale problems, our approach produces decompositions that outperform those produced by state‐of‐the‐art partitioners like METIS and even those that are manually constructed by domain experts. Copyright © 2017 John Wiley & Sons, Ltd.     

A time-domain symplectic method for finite viscoelastic cylinders

The symplectic method is introduced for boundary-condition problems of finite viscoelastic cylinders. On the basis of the state space formalism and the use of the Laplace integral transform, the general solution of the governing equations, zero- and nonzero-eigenvalue eigenvectors, are obtained. Since the eigenvectors are expressed in concise analytical forms, the adjoint symplectic relation of the Laplace domain is generalized to the time domain. Therefore, the particular solution and the eigenvector expansion method can be discussed directly in the eigenvector space of the time domain, without employing the iterative application of the inverse Laplace transformation. Using this method, various boundary conditions, the particular solution of nonhomogeneous equations, especially the interfacial continuity conditions of composite materials, can be conveniently described by combinations of the eigenvectors.