Generation of load dependent Ritz transformation vectors in structural dynamics

Abstract

The evaluation of linear dynamic response analysis of large structures by vector superposition requires, in its traditional formulation, the solution of a large and expensive eigenvalue problem. A method of solution based on a Ritz transformation to a reduced system of generalized coordinates using load dependent vectors generated from the spatial distribution of the dynamic loads is shown to maintain the high expected accuracy of modern computer analysis and significantly reduces the execution time over eigensolution procedures. New computational variants to generate load dependent vectors are presented and error norms are developed to control the convergence characteristics of load dependent Ritz solutions. Numerical applications on simple structural systems are used to show the relative efficiency of the proposed solution procedures.

Citation

Léger, P. and Wilson, E.L. (1987), "Generation of load dependent Ritz transformation vectors in structural dynamics", Engineering Computations, Vol. 4 No. 4, pp. 309-318. https://doi.org/10.1108/eb023709