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STOCHASTIC DYNAMICAL RESPONSE OF A NON-SMOOTH DYNAMICAL SYSTEM UNDER FILTERED WHITE NOISE

. The stochastic dynamic response of a spur gear pair model under filtered noise excitation is investigated. The spur gear pair is modeled as a single degree of freedom (SDOF) system in which nonlinear backlash and time-varying mesh stiffness as well as stochastic excitation are considered. Four cases are addressed, based on how the noise is incorporated in the loading terms. A first order ﬁlter is employed to generate various filtered noises with the same energy but different power spectrum. The combination of the SDOF gear model and the shaping filter leads to a three dimensional (3D) Markov model. The numerical path integration (PI) technique is adopted to obtain the probabilistic response of the gear model using an adaptive time-stepping method in order to increase the accuracy of the time integration. To model a narrow band noise excitation, a second order filter is applied to model the excitation, leading to a four dimensional (4D) Markov model. The results are verified by comparing with Monte Carlo simulations. The effect of the noise spectrum on the probabilistic response is evaluated for different loading cases.