P-bifurcation phenomena of the non-smooth modified rayleigh-duffing oscillator under the combined action of harmonic excitation and noise perturbation

Abstract

In this paper, the stochastic dynamics of a modified Rayleigh-Duffing oscillator with Coulomb frictional damping and elastic impact is investigated under combined harmonic and noise excitations. On the premise of retaining the non-smooth properties, a non-smooth steady-state probability density response numerical calculation method is introduced by taking advantage of Markov process. Utilizing this method, the stochastic P-bifurcation phenomena of oscillators without and with externally excitation are discussed in detail by inscribing changes in the topology of the steady-state probability density function. It is displayed that certain nonlinear damping coefficient and external excitation amplitude change the structure of the response, and that both the friction coefficient and the elastic coefficient of the contact surface induce stochastic P-bifurcation phenomena in systems without and with harmonic excitation, respectively. This study reveals the effect of non-smooth factors on the stability of the Rayleigh-Duffing oscillator.