Abstract
This work investigated the stochastic P-bifurcation (SPB) of a new class of unilateral impact vibration (VI) system under random parametric excitations, in which the elastoplastic stage of impact process is described by the restitution coefficient dependent with velocity model. By dint of the transformation of non-smooth, a new system without impact could be transformed from the original VI system. Subsequently, the stationary probability density functions (PDFs) of new system could be calculated by the associated equivalent nonlinear system. And then the critical parameters condition of SPB could be derived by means of the catastrophe theory. In the course of the study, it is verified that the new parameters induce the bifurcation of the system, which can be used to accurately measure the bifurcation behavior of the system quantitatively. And the system will tend to be stable under the precondition of enhancing the noise intensity. In addition, the validation of analytical results is examined by relative figures.
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