A progressive simultaneous iteration solution for dynamic element vibration analysis

Abstract

Development and employment of dynamic elements can result in substantial gain in solution convergence for vibration analysis, when compared with the usual finite element discretization. Efficient solution of the associated quadratic matrix eigenproblem is crucial in achieving a superior and relatively economical solution. This paper first describes a novel eigensolution of the quadratic matrix equation by a progressive simultaneous iteration method. Free vibration analysis results of a rectangular prestressed membrane are next presented in detail that provides an assessment of relative solution convergence and computing expenses of the two idealization procedures.