Effects of hysteretic and biviscous behaviors of magnetorheological damper on vehicle suspension systems

Magnetorheological (MR) dampers exhibit hysteretic and biviscous behaviours when subjected to dynamical loads. These behaviours have direct influences on vehicle suspension systems with MR dampers. First, the harmonic response of a quarter car system with MR damper is studied. Rewriting the govern equation of the system and introducing some assumptions, the coupling of the system variables uncoupled. With equivalent nonlinear method and harmonic balance method, the theoretical solution of harmonic response is obtained. The further results such as the amplitude-frequency relation and phase-frequency are also obtained. The numerical simulations validated the theoretical results. Second, the sprung and unsprung transmittances are deduced from the theoretical results. Then the effects of the hysteretic and biviscous behaviours on transmittances are evaluated. The biviscous behavior influences the sprung transmittances of the vehicle suspension system apparently and the unsprung transmittances slightly. The amplitudes of sprung transmittances decrease with the increasing of parameter p which can measure the biviscous behavior, especially when frequency ratio is at the point of the first resonant frequency, i.e. the sprung resonant frequency. The hysteretic behavior influences the sprung and unsprung transmittances in a complicated way. There is a good agreement between the theoretical results and numerical simulations.