A variational technique for the computation of the vibration frequencies of mechanical systems governed by nonsymmetric matrices

In this paper an algorithm for the solution of linear eigenvalue problems governed by ill-conditioned nonsymmetric matrices that are typical in dynamic structural analysis in the presence of nonconservative loads is proposed. The real eigenpairs (x,λ) are formulated as the minimizers of a suitable non-negative functional, which plays a role analogous to that of the Raleigh quotient for positive definite matrices. The proposed method, which is similar to a Rayleigh iterative scheme, has proven itself to be substancially unaffected by extremely high dispersions of the real eigenvalues. The method is illustrated by means of examples that correspond to beams subject to nonconservative loads.