The vibro-impact process is simplified by the instantaneous impact model,but the classical Newton's restitution coefficient model adopted brings errors in the calculation.In this paper,a modified restitution coefficient model is introduced to replace the classical Newton's model of restitution coefficient,and the stochastic response of a class of vibro-impact systems with bilateral barriers under broad-band noise excitation is investigated.Based on the energy levels of the system,its motion can be categorized into two types:non-colliding vibration and bilateral collision vibration.Subsequently,the average drift and diffusion coefficients for these two types of motion are determined using the energy envelope random averaging method.On this basis,the corresponding Fokker-Planck-Kolmogorov(FPK)equation is established and solved,leading to the steady-state response of the system.For illustration,the proposed method is applied to the Duffing oscillator.The effects of the yield velocity,interval and the noise excitations on the PDFs of stationary responses are examined,and the validation of analytical results is verified by the Monte Carlo simulation data.
the instantaneous impact modelrestitution coefficientvibro-impactwide-band noisestochastic averaging method
维普
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