Steady-State Response of a Dynamical System Under Combined Parametric and Forcing Excitations

[+] Author and Article Information
C. S. Hsu, W.-H. Cheng

Department of Mechanical Engineering, University of California, Berkeley, Calif.

J. Appl. Mech 41(2), 371-378 (Jun 01, 1974) (8 pages) doi:10.1115/1.3423296 History: Received January 01, 1973; Revised May 01, 1973; Online July 12, 2010


A linear dynamical system subjected to combined parametric and forcing excitations of periodic nature is governed by a system of inhomogeneous differential equations with periodic coefficients. Presented here is an explicit expression for the steady-state periodic response of such a system, given in terms of the fundamental matrix of the homogeneous system. Based upon this expression, specific analytic formulas of the steady-state response can be derived for some physical systems. For a general system where such an analytical determination is not feasible, the derived expression allows us to devise a straightforward numerical procedure which is particularly suited for computer evaluation and which is equally suited for high-order systems.

Copyright © 1974 by ASME
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