Evolutionary Dynamic of Quarter Car model: Regular and Chaotic Evolution

Abstract

Suspension systems in cars is very important for comfort driving and safety of passengers. Automobile industries design various suspension systems depending on the type of vehicle. Quarter-car models have been in use for years to study car dynamics. The objective of this article is to study the dynamics of evolution of a quarter-car model with each suspension system subjected to linear damping. The equation of motion of the system is described with a single degree of freedom. Stability criteria of steady states discussed analytically for the dimensionless equation in detail. Numerical simulation was performed to explore bifurcation phenomena and to obtain various regular and chaotic attractors. Lyapunov exponents, for chaotic and regular motions, calculated and presented through graphics. Numerical calculations extended to obtain Poincaré surfaces of sections and Poincaré maps which are significant to analyze evolutionary motion and clear indicators of regularity and chaos.