Abstract
The response of an oscillator with a nonlinear spring is considered when the excitation force is white noise filtered through a first-order, low-pass filter. When the damping is light, one term in the Fokker-Planck equation for the joint density function of displacement, velocity and acceleration is negligibly small. The resulting approximate Fokker-Planck equation can be solved exactly. An equivalent damping that keeps the power input to the oscillator constant is used to extend the range of validity of the approximate solution. A density function for the distribution of peaks is obtained that covers both narrow-band and broadband response. A numerical example of the nonlinear peak distribution is calculated for the case of an oscillator with a bilinear spring. The results are extended to the continuous case, using as an example a beam impacting springlike stops. [Work supported by NSERC.]
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