The dynamical analysis of a quarter car suspension based on the Kelvin–Voigt​ viscoelastic model with fractional order derivative is analytically and numerically studied in this paper. Depending on the non-dimensional quadratic stiffness parameter, the potential configuration associated with the system under study is possible to obtain monostable and, asymmetric bistable configurations. Thanks to the multiple time scale method, the effects of viscoelastic parameters on the vibration amplitude of the quarter car suspension model are analytically investigated and the numerical simulations confirmed the analytical results. Moreover, the vibration amplitude of the quarter car suspension model can display periodic and dissipative chaotic behaviors by varying the non-dimensional quadratic stiffness, the fractional-order, and the road profile parameters. One scroll and double scroll chaotic attractors are generated by varying the non-dimensional quadratic stiffness parameter. Finally, the threshold conditions for the appearance of homoclinic bifurcation (left well and right well) in the case of asymmetric bistable potential are investigated using Melnikov’s criterion. Melnikov’s predictions are validated numerically by using the basin of attraction of initial conditions. It is found that the decrease of fractional order contributes to increasing the regular motion domain up to a critical value of the fractional-order and after it, decreases rather.

本文对基于分数阶导数的 Kelvin-Voigt 粘弹性模型的四分之一汽车悬架的动力学分析进行了分析和数值研究。根据无量纲二次刚度参数，与所研究系统相关的潜在配置有可能获得单稳态和非对称双稳态配置。借助多时间尺度方法，分析研究了粘弹性参数对四分之一汽车悬架模型振动幅值的影响，并通过数值模拟验证了分析结果。此外，通过改变无量纲二次刚度、分数阶和道路剖面参数，四分之一汽车悬架模型的振动幅度可以显示周期性和耗散的混沌行为。通过改变无量纲二次刚度参数生成单涡旋和双涡旋混沌吸引子。最后，使用 Melnikov 准则研究了在非对称双稳态势情况下出现同宿分叉（左井和右井）的阈值条件。Melnikov 的预测通过使用初始条件的吸引力盆地进行了数值验证。发现分数阶的减少有助于将规则运动域增加到分数阶的临界值，并且在此之后，反而减少。使用 Melnikov 准则研究了在非对称双稳态电位情况下出现同宿分叉（左井和右井）的阈值条件。Melnikov 的预测通过使用初始条件的吸引力盆地进行了数值验证。发现分数阶的减少有助于将规则运动域增加到分数阶的临界值，并且在此之后，反而减少。使用 Melnikov 准则研究了在非对称双稳态电位情况下出现同宿分叉（左井和右井）的阈值条件。Melnikov 的预测通过使用初始条件的吸引力盆地进行了数值验证。发现分数阶的减少有助于将规则运动域增加到分数阶的临界值，并且在此之后，反而减少。