Nonclassically Damped Dynamic Systems: An Iterative Approach

[+] Author and Article Information
Firdaus E. Udwadia

University of Southern California, Los Angeles, CA 90089-1114

Ramin S. Esfandiari

California State University, Long Beach, CA 90840-5005

J. Appl. Mech 57(2), 423-433 (Jun 01, 1990) (11 pages) doi:10.1115/1.2892007 History: Received August 25, 1988; Revised June 01, 1989; Online March 31, 2008


This paper presents a new, computationally efficient, iterative technique for determining the dynamic response of nonclassically damped, linear systems. Such systems often arise in structural and mechanical engineering applications. The technique proposed in this paper is heuristically motivated and iteratively obtains the solution of a coupled set of second-order differential equations in terms of the solution to an uncoupled set. Rigorous results regarding sufficient conditions for the convergence of the iterative technique have been provided. These conditions encompass a broad variety of situations which are commonly met in structural dynamics, thereby making the proposed iterative scheme widely applicable. The method also provides new physical insights concerning the decoupling procedure and shows why previous approximate approaches for uncoupling nonclassically damped systems have led to large inaccuracies. Numerical examples are presented to indicate that, even under perhaps the least ideal conditions, the technique converges rapidly to provide the exact time histories of response.

Copyright © 1990 by The American Society of Mechanical Engineers
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