Random Vibration of a Nonlinear System With a Set-up Spring

[+] Author and Article Information
S. H. Crandall

Massachusetts Institute of Technology, Cambridge, Mass.

J. Appl. Mech 29(3), 477-482 (Sep 01, 1962) (6 pages) doi:10.1115/1.3640591 History: Received June 30, 1961; Online September 16, 2011


Several aspects of the problem of random vibration in nonlinear systems are discussed in terms of a particular set-up spring system. Exact solutions for the mean square response and the expected frequency of zero-crossings are obtained by means of the Fokker-Planck equation. These are compared with approximate solutions obtained from equivalent linearization techniques. The distribution of response peaks is then studied and a probability density is derived for the peaks on a relative frequency basis. The probability density of the response envelope is also obtained and the relationship between the two distributions is discussed.

Copyright © 1962 by ASME
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