Abstract
The paper deals with a quarter-car model with nonlinear damping and stiffness under white noise base excitation using the higher-order stochastic averaging method for analyzing approximate responses. Recently, a novel higher-order averaging procedure has been developed to find analytically the first-, second-, and third-order stationary joint probability density functions (PDF) of amplitude and full phase by solving the corresponding Fokker-Planck-Kolmogorov (FPK) equation, and it will be extended to the nonlinear quarter-car model. Accordingly, the mean-square responses such as the displacement, and velocity of the sprung mass can be obtained analytically. The influences of excitation intensity on the dynamic responses, as well as the variations of linear and nonlinear damping, are analyzed. A very satisfactory agreement is found between the accuracy of the solutions corresponding to higher-order stochastic averaging and that of Monte Carlo simulation.
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