Nonlinear Dynamic Response of Frames Using Lanczos Modal Analysis

Abstract

Modal reduction methods are a useful alternative to fully discrete matrix models for the efficient simulation of large dynamic response problems in frame analysis. The primary advantage of modal methods is computational efficiency, since they require less memory and fewer floating-point operations relative to conventional dynamic analyses of frames. The most important limitation of modal schemes is the difficulty in capturing strong nonlinear effects while retaining the simplicity of standard modal analysis algorithms. Modal methods obtained from inverse Lanczos iteration constitute a particularly elegant protocol for obtaining approximate time histories of response for nonlinear analyses of large frames and similar flexible structures. Examples underlining the strengths and weaknesses of Lanczos approximations are presented, and conclusions as to the utility of such modal reduction schemes for nonlinear dynamic analysis are drawn.