TY - JOUR ID - 71188 TI - Vibration of Road Vehicles with Non linear Suspensions JO - International Journal of Engineering JA - IJE LA - en SN - 1025-2495 AU - Nakhaie-Jazar, G. AU - Esmailzadeh, E. AU - Mehri, B. AD - Mechanical Engineering, Sharif University of Technology AD - Mathematics, Sharif University of Technology Y1 - 1997 PY - 1997 VL - 10 IS - 4 SP - 209 EP - 218 KW - Non KW - linear Suspensions KW - Vehicle Dynamics KW - Periodic Conditions KW - Fixed Point Theorem KW - Green's function DO - N2 - 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. UR - https://www.ije.ir/article_71188.html L1 - https://www.ije.ir/article_71188_2532b243ace5cbd50a15a61287ccd118.pdf ER -