Nonlinear Oscillations of Vehicle Tires with Hertzian Contact

The purpose of this work is to study the nonlinear vibrations induced due to wheel contact. The contact force is nonlinear and is considered to be caused due to a nonpolynomial $3∕2$ type of spring (Hertzian) as is commonly assumed to model wheel contact. Approximate periodic free vibration solutions are derived using an analytical technique based on the averaging method and is compared numerically. The case of the nonlinear wheel with nonlinear damping (van der Pol) is also studied and the possibility of the existence of a limit cycle is explored. The existence of initial condition dependent free periodic vibrations or a limit cycle under certain circumstances may be important for passenger comfort and noise generation or for vehicle safety as it may cause wear and tear of the mechanical components of the vehicle.