Mechanical Engineering, Sharif University of Technology
Mathematics, Sharif University of Technology
In order to investigate the effects of non-linear springs in vibrating behavior of vehicles, the independent suspension of conventional vehicles could be modeled as a non-linear single degree of freedom system. The equation of motion for the system would be a non-linear third order ordinary differential equation, when considering the elasticity of rubber bushings in joints of shock absorber. It is desirable that the system be stable, i.e., periodic inputs periodic outputs. In order to obtain the conditions that guarantee the existence of periodic solutions, and therefore, stable responses, the Schauder's fixed point theorem has been implemented to a general third order equation. Thus, the adapted conditions could be used for a wide range of dynamical systems. For the numerical analysis, a rapid convergence method has been developed, and used to solve the model. The correctness of periodic conditions and the numerical algorithm have been demonstrated.