【摘要】 基于瞬时变分原理 ,应用乘积型二元三次 B样条函数 ,建立了弹性地基板的样条动力方程 .引入样条参数及其对时间的导数作为状态变量 ,导出了状态方程 .对空间域 ,采用样条元法 ;对时间域 ,采用现代控制论中的状态空间法 .此外 ,建立了一种状态变量的递推计算格式 ,可以直接计算出动力响应量 .文末给出若干数值算例 ,计算结果表明本文方法的计算精度与效率是令人满意的 .更多还原

【Abstract】 Based on the instantaneous variational principle and the cubic B spline functions,the spline dynamic equation for plates on elastic foundation was established.The spline parameters and their derivatives with respect to time were taken as state variables, and the state space equation was derived.The spline finite element procedure was used in space domain and the state space technique was used in time domain.In addition,a state space recursive scheme was developed,so that the dynamic responses can be calculated directly.The numerical results were presented to show the accuracy and efficiency of this method.更多还原