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Stochastic bifurcation and dynamic reliability analyses of nonlinear MDOF vehicle system with generalized fractional damping via DPIM

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Abstract

The generalized fractional derivative is a useful tool for describing the mechanical property of viscoelastic dampers in vehicles. However, the complex integral form of the generalized fractional operator and the non-Markov property of fractional system make it challenging to perform stochastic dynamic analysis on multi-degree-of-freedom (MDOF) vehicle systems with generalized fractional damping. Thereby, the main purpose of this paper is to explore the stochastic dynamic characteristics of generalized fractional systems in the framework of the direct probability integral method (DPIM). To this end, a vehicle model with generalized fractional dampers is first constructed to simulate the driving process on uneven pavement, in which the random pavement roughness and discrete impulse excitation are described as continuous Gaussian white noise and discrete Poisson white noise, respectively. Then, the equivalent MDOF stochastic system of the model is derived, and the corresponding probability density integral equation (PDIE) is further established for uncertainty propagation. Benefiting from the historical memory of PDIE, a DPIM-based strategy is proposed to address the random vibration problem of the generalized fractional MDOF system. Finally, the stochastic bifurcation and dynamic reliability analyses of vehicle systems with generalized fractional damping are realized via the proposed strategy. The results indicate that the change of generalized fractional order, as a key design parameter, will cause stochastic bifurcation phenomenon and stochastic chaotic motion, which remarkably affects the vehicle ride comfort and driving safety.

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Data Availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Funding

The supports of the National Natural Science Foundation of China (Grant Nos. 12032008, 12102080), National Key R&D Program of China (Grant No. 2020YFB1709401) and Jiangsu Provincial Excellent Postdoctoral Program (Grant No. 2023ZB506) are much appreciated.

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Authors and Affiliations

  1. Center for Numerical Simulation Software in Engineering and Sciences, College of Mechanics and Engineering Science, Hohai University, Nanjing, 211100, China

    Hanshu Chen

  2. Department of Engineering Mechanics, State Key Laboratory of Structural Analysis, Optimization and CAE Software for Industrial Equipment, Dalian University of Technology, Dalian, 116024, China

    Hanshu Chen, Guohai Chen & Dixiong Yang

  3. School of Civil Engineering, Hefei University of Technology, Hefei, 230009, China

    Zeng Meng

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  1. Hanshu Chen
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Chen, H., Chen, G., Meng, Z. et al. Stochastic bifurcation and dynamic reliability analyses of nonlinear MDOF vehicle system with generalized fractional damping via DPIM. Nonlinear Dyn 112, 5291–5316 (2024). https://doi.org/10.1007/s11071-024-09313-4

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