Manufacturing Technology 2024, 24(6):886-900 | DOI: 10.21062/mft.2024.104

Nonlinear Stochastic Dynamics Analysis of Vehicle Bodies Based on the Direct Probability Density Integral Method

Qiangqiang Chen ORCID..., Jilei Zhou ORCID..., Chunkai Mu ORCID...
School of Transportation and Vehicle Engineering, Shandong University of Technology, Zibo, 255000, China

Manufacturing inaccuracies in vehicle suspension systems inevitably lead to uncertainties in the parameters of their structural components. Simultaneously, the road excitation impacting nonlinear vehicle systems exhibits pronounced randomness and time-variant characteristics. Consequently, it is crucial to conduct a stochastic dynamics analysis on nonlinear suspension systems, taking into account these uncertain factors. In this paper, a seven-degree-of-freedom (7-DOF) nonlinear suspension system dynamics model has been established. The stochastic process of road irregularities is simulated using the harmonic superposition method. Moreover, based on the direct probability density integral method, the stochastic dynamic equations of the nonlinear suspension system and their corresponding solution strategies have been developed and explored. Through MATLAB, the time-varying probability density function of the vibration response for a nonlinear vehicle suspension system was calculated under the combined effects of stochastic road irregularity excitation and random coupling of system structural parameters. Additionally, analyses were conducted on how different coefficients of variation and the intensity of nonlinearity in the suspension system influence the probability density of the output body displacement of the nonlinear vehicle suspension system. The research outcomes demonstrate that the direct probability density integral method offers superior efficiency and accuracy when computing nonlinear vehicle suspension systems. Furthermore, altering the coefficients of variation for various system parameters reveals that as these coefficients increase, the disparity in the probability density of body displacement becomes more pronounced, leading to more intense vehicle vibrations. Under soft nonlinear conditions with lower suspension spring stiffness, the probability density function of body displacement shifts slightly to the right with minimal change. However, under strong nonlinear conditions, body displacement significantly increases, resulting in diminished vibration isolation capabilities of the suspension system. This leads to severe jolts and a noticeable decline in ride comfort during vehicle operation.

Keywords: Direct probability density integral method, The road is not smooth, Harmonic superposition method, Nonlinear vehicle suspension system

Received: August 23, 2024; Revised: December 7, 2024; Accepted: December 17, 2024; Prepublished online: December 17, 2024; Published: December 21, 2024  Show citation

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Chen Q, Zhou J, Mu C. Nonlinear Stochastic Dynamics Analysis of Vehicle Bodies Based on the Direct Probability Density Integral Method. Manufacturing Technology. 2024;24(6):886-900. doi: 10.21062/mft.2024.104.
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