Analytical computation method for steady-state stochastic response of a time-delay nonlinear automotive suspension system. (15th September 2019)

• Record Type: Journal Article
• Authors: Wang, Wei; Song, Yuling
• Is Part Of: Mechanical systems and signal processing. Volume 131(2019)
• Page Start: 434
• Page End: 445
• Publication Date: 2019-09-15
• Subjects: Automotive suspension system -- Hamiltonian function -- Nonlinear stochastic vibration -- Time-delay feedback control -- Steady-state PDF; Structural dynamics -- Periodicals; Vibration -- Periodicals; Constructions -- Dynamique -- Périodiques; Vibration -- Périodiques; Structural dynamics; Vibration; Periodicals; 621
• DOI: 10.1016/j.ymssp.2019.05.061
• Languages: English
• ISSNs: 0888-3270

Abstract

Highlights: An analytical method for the PDFs of a time-delay nonlinear suspension is proposed. Time-delay terms are reasonably treated based on averaged angular frequency. The stochastic responses of the model with nonlinear conservative term are solved. Stochastic response properties and delayed time influences are investigated. Theoretical results are verified by computations, comparisons and analyses. 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 Itô 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 Itô 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.