Abstract
Abstract A novel analytical computation method of steady-state probability density function (PDF) is presented to solve the stochastic response of a time-delay nonlinear automotive suspension system. In accordance with actual projects, a stochastic dynamics model of the automotive suspension system is established which includes cubic nonlinear restoring force, time-delay feedback control term and random road excitation simulated by white Gaussian noise. Based on the averaged angular frequency derived from Hamiltonian function of the nonlinear conservative system associated with the established stochastic dynamics model, the original system is transformed into a stochastic differential dynamics system without time-delay terms. By using generalized harmonic function-based stochastic averaging method and deterministic averaging method, the averaged Ito stochastic differential equation associated with the transformed system is obtained. Through solving the averaged Fokker-Planck-Kolmogorov equation established by drift and diffusion coefficients of the Ito equation, the steady-state PDFs of stochastic response amplitude and systematic energy as well as the steady-state joint PDF of stochastic response are obtained. All of the analytical results are verified by digital simulations.
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