Response Analysis Of Nonlinear Systems Under Gaussian And Poisson White Noise

Response analysis is always a hot spot in the study of nonlinear stochastic dynamics.In this paper,the random response of several types of nonlinear systems under the Gaussian and Poisson white noise excitation is studied.In the first chapter,we briefly introduce the origin of stochastic dynamics,the research development of nonlinear stochastic dynamics,and the research status of stochastic averaging method.In the second chapter,Sampling technique of typical models of random excitations and corresponding Monte Carlo simulation method are presented.Then the stochastic averaging method used here is introduced.In the third chapter,based on the stochastic averaging method,the response of a one-degree-of-freedom vibro-impact system with Hertz damping barrier in one side on the other side and a rigid barrier in the other side under external excitation of Poisson white noise is studied,The response of a Duffing-Van der Pol-Oscillator with asymmetric bilateral barrier of an elastic wall and a rigid wall under external and parametric excitations of Poisson white noise is studied then.At last,response of a vibro-impact system with both sides of Hertz damping barriers under parametric and external and parametric excitations of Poisson and Gaussian white noises is studied.To solve the problems listed above,the equations of motion are changed to obtain a continuous phase curve by using the Zhuravlev transform.By using the stochastic averaging method,the average generalized FPK equations of these systems are obtained.Then the perturbation method is used to work out the probability density function(PDF)of system energy.Effects of different parameters on these results are discussed.In the fourth chapter,the influence of the friction force and the nonlinear damping force on the random response of the Van der Pol oscillator is presented.Firstly,the averaged generalized FPK equation of the system is obtained by the stochastic averaging method.Then the PDF of the system energy is obtained by the perturbation method.At the same time,the theoretical results are discussed and compared with those from the Monte Carlo simulations.It is found that along with the increase of the variance of intensity of random impulses,the variance of the system energy and displacement increase.With the change of some small parameters,the probability density of the system displacement has a tendency to change from single peak to double peak.The fifth chapter studies the transient response of the quasi linear systems under Gaussian and Poisson white noise excitation.Based on the stochastic averaging method and Galerkin method,the transient response of the quasi-linear systems is obtained.The probability density curves of the displacement and system energy at different points in time are obtained.The feasibility of the method is verified by Monte Carlo method.