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SUMMARYBased on the Neumann series expansion and epsilon-algorithm, a new eigensolution reanalysis method is developed. In the solution process, the basis vectors can be obtained using the matrix perturbation or the Neumann series expansion to construct the vector sequence, and then using the epsilon algorithm table to obtain the approximate eigenvectors. The approximate eigenvalues are computed from the Rayleigh quotients. The solution steps are straightforward and it is easy to implement with the general finite element analysis system. Two numerical examples, a 40-storey frame and a chassis structure, are given to demonstrate the application of the present method. By comparing with the exact solutions and the Kirsch method solutions, it is shown that the excellent results are obtained for very large changes in the design, and that the accuracy of the epsilon-algorithm is higher than that of the Kirsch method and the computation time is less than that of the Kirsch method.

SUMMARYIn practical engineering, it is difficult to obtain all possible solutions of dynamic responses with sharp bounds even if an optimum scheme is adopted where there are many uncertain parameters. In this paper, using the interval finite element (IFE) method and precise time integration (PTI) method, we discuss the dynamic response of vibration control problem of structures with interval parameters. With matrix perturbation theory and interval arithmetic, the algorithm for estimating upper and lower bounds of dynamic response of the closed-loop system is developed directly from the interval parameters. Two numerical examples are given to illustrate the application of the present method. The example 1 is used to show the applicability of the present method. The example 2 is used to show the validity of the present method by comparing the results with those obtained by the classical random perturbation method.