A CLUSTER SERIES EXPANSION TECHNIQUE FOR SOLVING VIBRATION PROBLEMS

A cluster series expansion technique for spectral solution of vibration problems is presented. In this technique the eigenfunction approximations are composed of clusters of single basis functions instead of the classical Fourier series of single basis functions. To realize the cluster expansion an alternating fixed-free subspace strategy is used to improve the coefficients of the single basis functions inside the clusters. This strategy generates a family of m -step iterative algorithms solving large dense matrix eigenproblem of order m. n as a few dense matrix eigenproblems of ordern +(m−1)ℓ, where ℓ denotes the number of computed eigenvalues. The computational behaviour of the proposed m -step algorithms is investigated by solving matrix eigenproblems up to the order 3600 by using them -step algorithms for m=2, 3, 4, 5.