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A new method for computing the upper and lower bounds on frequencies of structures with interval parameters. (English) Zbl 0820.73041

Summary: We give a method for computing the upper and lower bounds on frequencies of stuctures with bounded uncertain (or interval) parameters. The stiffness matrix and the mass matrix of structures, whose elements have the initial errors, are unknown except for the fact that they belong to given bounded matrix sets. The set of possible matrices can be described by the interval matrix. By means of the stationary condition on Rayleigh quotient and the minimax theorem on eigenvalues, the generalized eigenvalue problem of structures with bounded uncertain parameters can be transformed into two different generalized eigenvalue problems. The numerical results indicate that the proposed method is effective.

MSC:

74H45 Vibrations in dynamical problems in solid mechanics
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