Non-stationary stochastic response determination of vibro-impact system under combination harmonic and Gaussian white noise excitations

Abstract

Vibro-impact system (VI-S) have demonstrated their potential to contribute to engineering practice throughout the last few years. Nonetheless, their scope of application are still very limited. One of a primary reason is that dynamic behaviors of VI-S under the combination of deterministic period excitations (deterministic period excitation) and random noises (random noises) are not entirely understood. Toward this, the radial basis function neural network (rbfnn) is used to analyze dynamical behaviors evolution of VI-S under deterministic period excitation combined with random noises. To illustrate the potential of the proposed scheme, two classical examples of Mathieu–Duffing oscillator and Duffing–Rayleigh oscillator are considered. The evolutionary of dynamics behaviors and stochastic P-bifurcation phenomenon are examined through a qualitative change of the probability distribution, which indicates that system parameters and noise intensity, respectively, can be treated as bifurcation-induced parameters. Besides, numerical results are also carried out to confirm the accuracy of semi-analytical prediction.