Resonance, stability and period-doubling bifurcation of a quarter-car model excited by the road surface profile

Stability and the steady states of the transverse motion of a quarter-car model excited by the road surface profile with non-symmetric potential is investigated. Initially, a set of slow-flow equations is derived using the method of multiple-time scales directly to the governing equation, governing the amplitudes and phases of approximate long time response of these oscillators, by applying an asymptotic analytical method. Determination of several possible types of steady-state motions is then reduced to solution of sets of algebraic equations. For all these solution types, appropriate stability analysis is also performed. In the second part of the study, this analysis is applied to an example mechanical system. First, a systematic search is performed, revealing effects of system parameters on the existence and stability properties of periodic motions. Frequency-response as well as forced-response diagrams are presented and attention is focused on understanding the evolution and interaction of the various solution branches as the external forcing and nonlinearity parameters are varied. Finally, numerical integration of the equations of motion demonstrates that the system exhibits period-doubling bifurcation or chaotic response for some parameter combinations.