Abstract
Vibro-impact machines are found increasingly broad application in various sectors of the world. And the mass disturbance exists in the process of impact, which refers to the variable mass system that is a common phenomenon in life. With the development of micro-electronic and nanotechnology, it is essential to investigate the effect of mass disturbance on this random vibro-impact system response. The stationary system response is the main topic of the manuscript. In the light of the discontinuity of vibro-impact system, the nonsmooth transformation is introduced to overcome the discontinuity. Then the stochastic averaging technique is applied to the transformed stochastic variable mass system. The approximate analytical response can be obtained by solving associated Fokker–Planck–Kolmogorov equation. A Van der Pol variable mass vibro-impact system is given to illustrate the application and availability of this method. Meanwhile, stochastic P-bifurcation is studied, and a reasonable interpretation is given to explain the procedure of stochastic P-bifurcation.
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