【摘要】 本文给出了粘弹性薄板动力响应问题的多重互易法(MRM)。首先在Laplace变换区域中得到了由重调和算子基本解序列给出的粘弹性板动力响应问题的MRM方法,再利用改进的Bellman反变换技术,求得原问题的解。讨论了MRM方法中的迭代误差估计。文末给出了数值算例,计算表明该方法具有较高精度和较快收敛性。适用于长时间的动力问题的计算。更多还原

【Abstract】 Multiple Reciprocity Method (MRM) for solving dynamics response of viscoelastic thin plate is proposed in this paper. The sequence of fundamental solutions for biharmonic operator is first used to derive the MRM for solving dynamics response of viscoelastic thin in the Laplace transform domain. Then, by applying the improved Bellman’s numerical inversion of Laplace transform, the solution of original problem is obtained. Next, the iterative error estimation for MRM is discussed. Finally the numerical examples show that our method has higher accuracy and faster convergence. It’s suitable for the solution of the dynamic problem with a lone time span.更多还原