The Application of the Ritz Averaging Method to Determining the Response of Systems with Time Varying Stiffness to Harmonic Excitation

[+] Author and Article Information
M. Benton

Engineering R&D Division, E.I. DuPont, Wilmington, Del. 19898

A. Seireg

Department of Mechanical Engineering, The University of Wisconsin, Madison, Wisc. 53706

J. Mech. Des 102(2), 384-390 (Apr 01, 1980) (7 pages) doi:10.1115/1.3254755 History: Received May 29, 1979; Online November 17, 2009


Parametric vibrations occur in many mechanical systems such as gears where the stiffness variation and external excitations generally occur at integer multiples of the rotational speed. This paper describes a procedure based on the Ritz Averaging Method for developing closed form solutions for the response of such systems to harmonic excitations. Although the method is illustrated in the paper by the case of a linear system with harmonic stiffness fluctuation (defined by Mathieu’s equation) it can be readily applied to determine approximate solutions for systems with nonlinear characteristics and any periodic variations of parameters.

Copyright © 1980 by ASME
Topics: Stiffness
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