Solution methods for eigenvalue problems in structural mechanics
Klaus‐Jürgen Bathe, Edward L. Wilson · International Journal for Numerical Methods in Engineering · 1973
Abstract A survey of probably the most efficient solution methods currently in use for the problems K ϕ = ω 2 M ϕ and K Ψ = λ K G Ψ is presented. In the eigenvalue problems the stiffness matrices K and K G 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.