Abstract
We have combined the techniques of statistical and harmonic linearization to develop a linearized approximation theory for the calculation of the second-order statistics (i.e., autocorrelation functions and spectral densities) of nonlinear systems driven by both random and periodic forces. For the special case of a Duffing oscillator (a damped anharmonic oscillator with a cubic nonlinearity) driven by Gaussian white noise and by a sinusoidal force, explicit expressions for the renormalized (linearized) frequency, the autocorrelation function, and the spectral density of the oscillator displacement in terms of all the system parameters have been derived. We have determined the region of the parameter space in which the applied periodic force has a significant influence on the second-order statistics of the oscillator.
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This research was supported by the Office of Naval Research, by the National Science Foundation under grant No. CHE78-21460 and by a grant from Charles and Reneé Taubman.
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Bulsara, A.R., Lindenberg, K. & Shuler, K.E. Spectral analysis of a nonlinear oscillator driven by random and periodic forces. I. Linearized theory. J Stat Phys 27, 787–808 (1982). https://doi.org/10.1007/BF01013448
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DOI: https://doi.org/10.1007/BF01013448