Power Spectral Density of the Response of a Nonlinear System to Random Excitation

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Abstract
The damping and spring forces acting on a single-mode oscillator are considered as a power series in velocity and displacement, respectively. The power spectral density of the response of such a system is derived through a perturbation procedure. Moreover, the mean-square response is calculated when the excitation is an ideal white Gaussian process. The influences of both nonlinear damping and stiffness forces on the behavior of the system are discussed.

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