SOLUTION OF EIGENVALUE PROBLEM FOR NONCLASSICALLY DAMPED SYSTEM WITH MULTIPLE EIGENVALUES

초록

An efficient solution method is presented to solve the eigenvalue problem arising in the dynamic analysis of nonclassically damped structural systems with multiple eigenvalues. The proposed method is obtained by applying the modified Newton-Raphson technique and the orthonormal condition of the eigenvectors to the quadratic eigenvalue problem. In the iteration methods such as the inverse iteration method and the subspace iteration method, singularity may be occurred during the factorizing process when the shift value is close to an eigenvalue of the system. However, even if the shift value is an eigenvalue of the system, the proposed method guarantees nonsingularity, which is analytically proved. A numerical example is also presented to demonstrate the effectiveness of the proposed method and the results are compared with subspace iteration method and the Lanczos method.