Statistical Linearization and Large Excitation of Nonlinear Stochastic Mechanical Systems

Abstract

In mechanical systems nonlinear effects due to cubic stiffness and Coulomb friction are often observed. The behavior of such systems is analysed for different colored noise excitations, particularly the softening Duffing oscillator. The statistical linearization is used for obtaining mean square responses and then the mean square jump phenomenon is discussed. It is shown that the jumps can occur in the Duffing oscillator with softening stiffness. It is also shown that the softening oscillator does not exhibit stationary response for some range of the excitation bandwidth. Moreover, in this range the softening system may exhibit a nonstationary response increasing to infinity with the time. In the case of stationary responses the agreement between simulation and statistical linearization results is very good. The response of a single-degree-of-freedom spring-mass system with viscous and Coulomb friction with colored noise excitation using the technique of statistical linearization is also discussed. Further a good agreement between the simulation and analytical results is observed.