Response Analysis Of Duhem Hysteretic System Under Random Excitation Of Poisson White Noise

In the field of random vibration,response analysis of hysteretic system is a hot area.Many structures and materials exhibit hysteretic characteristics under loads,such as smart materials,piezoelectric materials,structural damping devices,plastic hinges in steel frames,shape memory alloys,and so on.Therefore,the study on stochastic dynamics of hysteretic system is very important.Now,many different models have been established for various hysteretic phenomena and the parameters of each systems are dynamically optimized.However,most of the stochastic response analysis is based on Gaussian white noise,and the stochastic response of system subject to Poisson white noise is relatively few.In this paper,random response of Duhem hysteresis system is studied.Stationary response probability density function is obtained by using the stochastic averaging method and the perturbation method.Firstly,the main methods on random vibration of nonlinear system and development of response analysis of hysteretic system are reviewed.After giving the definition of Poisson white noise and the Monte Carlo method,the equivalent nonlinearization method and the stochastic averaging method are introduced.Secondly,the non-hysteretic equivalent nonlinear equation of motion is established for the Coleman-Hodgdon hysteresis model.The expressions of potential energy and dissipation energy are obtained.By using the Monte Carlo simulation method,the difference between the equivalent nonlinear system and the original system under different parameters is analyzed.Thirdly,stationary response of Yar-Mohammad bilinear hysteresis system under Poisson white noise excitation is studied.The average generalized FPK equation is deduced by using stochastic averaging method.The perturbation method is used to solve the equation.The stationary response probability densities of energy and displacement are obtained.Then,the solution procedure is extended to problem of response analysis of Duhem hysteretic system under Poisson white noise excitation.The accuracy of the solution is verified by an example.Finally,stationary response of a vibro-impact system with bilinear hysteresis and bilateral Herzt elastic wall is studied under the Poisson white noise excitation by using the method given here.