Application of Ultraspherical Polynomials to Nonlinear Forced Oscillations

[+] Author and Article Information
Y. King Liu

Department of Engineering Mechanics, University of Michigan, Ann Arbor, Mich.

J. Appl. Mech 34(1), 223-226 (Mar 01, 1967) (4 pages) doi:10.1115/1.3607636 History: Received March 28, 1966; Revised September 12, 1966; Online September 14, 2011


Approximate solutions to the conservative free-oscillation problem were obtained recently [1–4] through the use of ultraspherical polynomials. The present paper extends the technique to forced oscillations governed by

ẍ + g(ẋ) + f(x) = F0 sin pt + F1
Very accurate results are obtained either by setting the ultraspherical polynomial index λ = 0 or, better yet, by restricting the choice of λ such that the solution to the forced problem is a perturbation from the nonlinear free oscillation solution. Examples are given.

Copyright © 1967 by ASME
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