Solution methods for eigenvalue problems in structural mechanics

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Abstract
A survey of probably the most efficient solution methods currently in use for the problems Kϕ = ω2Mϕ and KΨ = λKGΨ is presented. In the eigenvalue problems the stiffness matrices K and KG and the mass matrix M can be full or banded; the mass matrix can be diagonal with zero diagonal elements. The choice is between the well‐known QR method, a generalized Jacobi iteration, a new determinant search technique and an automated sub‐space iteration. The system size, the bandwidth and the number of required eigenvalues and eigenvectors determine which method should be used on a particular problem. The numerical advantages of each solution technique, operation counts and storage requirements are given to establish guidelines for the selection of the appropriate algorithm. A large number of typical solution times are presented.

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