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

• Published in: Applied mathematical modelling Vol. 16; no. 3; pp. 148 - 154
• Main Authors: Alliney, S., Laudiero, F., Savoia, M.
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Inc 1992; Elsevier Science
• Subjects: eigenvalue computation; Exact sciences and technology; Fundamental areas of phenomenology (including applications); mathematical models; mechanical systems; nonconservative loads; Physics; projection technique; Solid mechanics; structural analysis; Structural and continuum mechanics; variational methods; vibration; vibration frequencies; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); variational methods; projection technique; vibration frequencies; eigenvalue computation; nonconservative loads; Projection method; Variational calculus; Follower force; Eigenvalue problem; Vibration; Beam(mechanics)
• ISSN: 0307-904X
• DOI: 10.1016/0307-904X(92)90066-C

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.