A Numerical Method for Free Vibration Analysis of Structures with Small Design Changes : 2nd Report: Analysis of Degenerate or Nearly Degenerate Cases by a Subspace Technique

抄録

This paper presents a numerical method for free vibration analysis of structures with small design changes or perturbations. The proposed method is an extension of the iteration scheme introduced in the first report of this paper. A subspace technique is employed to deal with variation of degenerate or nearly degenerate eigenvalues of the unperturbed problems. The algorithm is designed such that it can be easily implemented in large-scale finite element computations. To see the effectiveness and fundamental properties of the proposed method, some numerical results are given for lateral vibration problems of a cantilever beam, a circular plate, and a parallelogramic membrane. It is shown that the present approach can actually analyze the separation of degenerate eigenvalues. Furthermore, it can improve the convergence behavior of the iteration process when it is compared with the method in the first report.