Analysis of Vehicle Vibration Considering Fractional Damping in Suspensions and Tires

Vehicle dynamics play a crucial role in assessing vehicle performance, comfort, and safety. To precisely depict the dynamic behaviors of a vehicle, fractional damping is employed to substitute the conventional damping in suspensions and tires. Taking the fractional damping into account, a four-degrees-of-freedom vehicle model is developed, which encompasses the vertical vibration and pitch motion of the vehicle body, as well as the vertical motions of the front and rear axles. The vibration equations are solved in the Laplace domain using the transfer function method. The validity of the transfer function method is verified through comparison with a benchmark case. The vibrations of the vehicle are analyzed under the effects of suspension and tire properties, pavement excitation, and vehicle speed. The assessment methods employed include the time-domain vibration response, amplitude–frequency curves, phase diagrams, the frequency response function matrix, and weighted root mean square acceleration. The results show that the larger fractional order results in higher energy dissipation. Elevated values of the fractional order α, suspension stiffness, and the damping coefficient contribute to greater stable vibration amplitudes in vehicles and a consequent degradation in ride comfort. Higher tire stiffness reduces vehicle vibration amplitude, while the fractional order β and tire damping have a negligible effect. Moreover, increased vehicle speed and a greater pavement input amplitude adversely affect ride comfort.