Abstract
A modified stochastic averaging method on a Duffing-Rayleigh oscillator with strongly nonlinearity subject to Gaussian colored noise excitation was proposed. The so-called He’s energy balance method was applied to obtain the averaged frequency of the conservative system. Subsequently, the stochastic averaging method of strong nonlinearity was used. The modified method can offer more concise approximate expressions of the drift and diffusion coefficients without weakening the accuracy of predicting the responses of the systems too much. The stationary responses of probability density of amplitudes, together with joint probability density of displacement and velocity are studied to verify the presented approach. The reliability of the systems was also investigated to offer further support. Digital simulations were carried out and the output of that are coincide with the theoretical approximations well.
Highlights
IntroductionStochastic vibration has drawn accelerating interests. An effective and powerful method dealing with stochastic vibrations is the stochastic averaging method
In recent half century, stochastic vibration has drawn accelerating interests
The stochastic averaging method initialized by Landau and Stratonovich [1] and Khasminskii [2] is called as the method of quasi-conservative averaging
Summary
Stochastic vibration has drawn accelerating interests. An effective and powerful method dealing with stochastic vibrations is the stochastic averaging method. Xu and Chung [13] have proposed a method to deal with noise-free strongly nonlinear Oscillators based on the so-called generalized harmonic functions This method has been extended by Zhu and Huang [14, 15] to handle strongly non-linear oscillators with lightly linear and (or) non-linear damping subject to weakly external and (or) parametric excitations of wide-band random processes. A typical Duffing-Vanderpol oscillator has been studied by this method [15], the stability of the stationary response and the stochastic Hopf-bifurcation has been investigated The precision of this method has been verified by digital simulations. There remains a need to shorten the expressions of the drift coefficient and diffusion coefficient without weakening the accuracy too much This method is mainly applied on white noise or non-white wide-band random. Digital simulations were carried out and the results were consistent with the theoretical approximations
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