Multiple Reciprocity Method (MRM) For Solving Dynamics Response Of Viscoelastic Thin Plate And Its Convergence Analysis

In this paper, firstly we present some results about of conventional BEM,and Multiple Reciprocity Method (MRM)for solving dynamics response of Viscoelastic thin plate is given the whole plane expression and boundary integral equation for MRM, next we prove that the solution of the boundary integral equation obtained by MRM is the same as the one derived from the conventional fundamental solution of boundary value problem. Applying variational method we analyze the existence and uniqueness for the solution of the corresponding boundary variational equation, truncated MRM boundary variational equation, and approximation truncated MRM boundary variational equation in detailed. We obtain the error estimation for various approximation solutions and construct the boundary integral method with constraint. We explain the principle for choosing the mesh size and the truncated number in MRM .Finally the numerical examples show that the theoretical analysis is accord with the numerical experiment result . By this way we perfectly discuss the MRM for the dynamic response of viscoelastic thin plate and its convergence analysis.