弹性动力学的多变量响应问题的解法

Method of Multivariable Responses for Elastic Dynamics

基于瞬时混合变分原理与乘积型二元三次 B样条函数 ,以板壳为例 ,建立样条动力方程。引入样条参数及其对时间的导数作为状态变量 ,导出状态方程。对空间域采用混合样条元法 ,对时间域采用现代控制论中的状态空间法。文中还建立了一种状态变量的递推计算格式 ,可以直接计算出多变量动力响应值。数值计算结果表明 ,本文方法的计算精度与效率是令人满意的。本文方法对计算多输入与多输出 ,时不变与时变系统和线性与非线性系统等多变量动力响应问题 ,有广阔的应用与发展前景。

This paper presents a method of determining multivariable response of elastic dynamics. Based on instantaneous mixed variational principle and spline interpolate functions, the spline equation of motion is derived. The spline parameter and its derivative are taken as state variables. The spline finite element procedure is used in space domain and the state space technique in time domain respectively. An effective recursive scheme is developed that multivariable dynamical responses including displacements, velocities, accelerations and internal forces can be obtained directly. Numerical results are presented to demonstrate the accuracy and efficiency of the method. For the problems of multi-input or multi-output, time-invariant or time-variant, linear or nonlinear systems, the method would have prospective wide applications and developments.