粘弹性薄板动力响应问题的多重互易法  

Multiple Reciprocity Method for Solving Dynamics Response of Viscoelastic Thin Plate

作　　者：丁睿[1] 姚林泉[1] 李挺[1] 

机构地区：[1]苏州大学数学科学学院,江苏苏州215006

出　　处：《工程数学学报》2005年第6期1006-1012,共7页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10201026)江苏省高校自然科学基金(04KJB110117)苏州大学优秀青年骨干教师基金(R2317131).

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。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 long time span.

关 键 词：动力响应 粘弹性 多重互易方法(MRM) 

分 类 号：O175.8[理学—数学]