Abstract: 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.

Key words: vibrating beam, inverse problem, real symmetric five diagonal matrix, generalized eigenvalue, defective eigenpair