Response analysis for a vibroimpact Duffing system with bilateral barriers under external and parametric Gaussian white noises

• The stationary response of a vibroimpact Duffing oscillator with two barriers is considered under external and parametric Gaussian white noise random excitations.
• According to the levels of the system energy, the possible motions of the unperturbed vibroimpact system are discussed.
• Stationary responses are obtained by a stochastic averaging method for energy envelope.
• Results obtained from the proposed procedure are validated by directly numerical simulation.

In this paper, a vibroimpact Duffing oscillator with two barriers that are symmetrical with respect to the equilibrium point of the system is considered for the cases of external and parametric Gaussian white noise random excitations. According to the levels of the system energy, the motions of the unperturbed vibroimpact system are divided into two types: oscillations without impacts and oscillations with alternate impacts on both sides. Then, under the assumption that the vibroimpact Duffing system is quasi-conservative, the stochastic averaging method for energy envelope is applied to obtain the averaged drift and diffusion coefficients for the two types of motions, respectively. The Probability Density Functions (PDFs) of stationary responses are derived by solving the corresponding Fokker-Plank-Kolmogorov (FPK) equation. Lastly, results obtained from the proposed procedure are validated by directly numerical simulation. Meanwhile, effects of the position of bilateral barriers and the random excitations on the PDFs of the stationary responses are also discussed.