Responses of Duffing-Van der Pol vibro-impact system excited by random narrow-band noise

【作者】 黄冬梅；

【机构】 西北工业大学理学院应用数学系；

【摘要】 We investigate the responses of a non-linear vibro-impact oscillator with a one-sided barrier subject to random narrow-band excitation. With the help of a non-smooth variable transformation and Dirac delta function, the original impact system is reduced to a system without velocity jumps. By using the Krylov-Bogoliubov averaging method, the frequency response equation is obtained for the deterministic case. Then an iterative calculation equation for the mean-square amplitude is obtained for the stochastic case. Theoretical results are verified by direct numerical simulations. The influence of system parameters as well as the bandwidth of random noise on the steady-state response are discussed. The phenomenon of stochastic jump is observed. Moreover, as bandwidth of random noise increases the pervasion of the phase trajectories strengthens, and then destroys the topological property of the phase trajectories.更多还原

【Abstract】 We investigate the responses of a non-linear vibro-impact oscillator with a one-sided barrier subject to random narrow-band excitation. With the help of a non-smooth variable transformation and Dirac delta function, the original impact system is reduced to a system without velocity jumps. By using the Krylov-Bogoliubov averaging method, the frequency response equation is obtained for the deterministic case. Then an iterative calculation equation for the mean-square amplitude is obtained for the stochastic case. Theoretical results are verified by direct numerical simulations. The influence of system parameters as well as the bandwidth of random noise on the steady-state response are discussed. The phenomenon of stochastic jump is observed. Moreover, as bandwidth of random noise increases the pervasion of the phase trajectories strengthens, and then destroys the topological property of the phase trajectories.更多还原