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

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.