Stability and Limit Cycles of Parametrically Excited, Axially Moving Strings

[+] Author and Article Information
E. M. Mockensturm

Department of Mechanical Engineering, University of California, Berkeley, CA 94720

N. C. Perkins, A. Galip Ulsoy

Department of Mechanical Engineering and Applied Mechanics, University of Michigan, Ann Arbor, MI 48109

J. Vib. Acoust 118(3), 346-351 (Jul 01, 1996) (6 pages) doi:10.1115/1.2888189 History: Received April 01, 1994; Revised December 01, 1994; Online February 26, 2008


Tension fluctuations are the dominant source of excitation in automotive belts. In particular designs, these fluctuations may parametrically excite large amplitude transverse belt vibrations and adversely impact belt life. This paper evaluates an efficient discrete model of a parametrically excited translating belt. The efficiency derives from the use of translating string eigenfunctions as a basis for a Galerkin discretization of the equations of transverse belt response. Accurate and low-order models lead to simple closed-form solutions for the existence and stability of limit cycles near parametric instability regions. In particular, simple expressions are found for the stability boundaries of the general nth-mode principal parametric instability regions and the first summation and difference parametric instability regions. Subsequent evaluation of the weakly nonlinear equation of motion leads to an analytical expression for the amplitudes (and stability) of nontrivial limit cycles that exist around the nth-mode principal parametric instability regions. Example results highlight important conclusions concerning the response of automotive belt drives.

Copyright © 1996 by The American Society of Mechanical Engineers
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