特征值问题的边界形状灵敏度

研究连续系统振动特征值问题的边界形状灵敏度满足什么方程和边界条件，如何离散化作近似计算结果表明：如果采用相同的有限单元剖分模式，边界形状灵敏度方程和特征值问题方程具有相同的系数矩阵，但前者是非齐次方程，后者是齐次方程；前者需要施加非齐次边界条件，后者施加齐次边界条件。

SHAPE SENSITIVITY ANALYSIS OF THE EIGENPROBLEM

This paper deals with eigenproblem sensitivity analysis with respect to boundary shape. It shows how to obtain the distributed parameter differential equations plus boundary conditions which govern the eigenproblem sensitivity before the structure is discretized, and how to obtain the solution to them using finite element methods. This paper points out that the distributed parameter differential equations plus boundary conditions, which govern the eigenproblem sensitivity, are just the non-homogeneous ones associated with the eigenproblem. Thus, the eigenpair sensitivity problem and its original eigenproblem have the same system matrices (mass matrixand stiffness matrix), when finite element methods are applied to them, but different boundary condition. At the end, this paper gives three examples to illustrate the idea presented.