缺损特征对的梁振动反问题

Inverse Problem for the Vibrating Beam from Its Defective Eigen-pair

针对梁的离散化模型的刚度矩阵是五对角矩阵,梁振动反问题的实质是实对称五对角矩阵的特征值反问题,利用主子阵和缺损特征对研究实对称五对角矩阵的广义特征值反问题,讨论了有解的条件,并给出了解的表达式.

In view of the stiffness matrix of the discrete vibrating beam is a real symmetric five-diagonal matrix and the substance of the inverse problem for the vibrating beam is the inverse eigenvalue problem of the real symmetric five-diagonal matrix, a kind of inverse generalized eigenvalue problem is proposed, which is the reconstruction of real symmetric five-diagonal matrix from its defective eigen-pair and a principal submatrix. The conditions for the solvability of the problem are given.