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.
Random Vibration of a Nonlinear System With a Set-up Spring
S. H. Crandall
Massachusetts Institute of Technology, Cambridge, Mass.
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Crandall, S. H. (September 1, 1962). "Random Vibration of a Nonlinear System With a Set-up Spring." ASME. J. Appl. Mech. September 1962; 29(3): 477–482. https://doi.org/10.1115/1.3640591
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