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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 .
Based on the principle of instantaneous variational variation, the spline kinetic equation of the elastic foundation plate is established by using the product-type bivariate cubic B-spline function. The spline parameter and its derivative with respect to time are introduced as state variables, and the equation of state is derived. , The spline element method is adopted, and the state space method of modern cybernetics is used for the time domain. In addition, a recursive computation formula of state variables is established, which can directly calculate the dynamic response.Several numerical examples The calculation results show that the calculation accuracy and efficiency of this method are satisfactory.