SHAPE SENSITIVITY ANALYSIS OF THE EIGENPROBLEM
特征值问题的边界形状灵敏度

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.