Control and dynamics of quarter-car models with dual-rate damping

Dynamics of a controlled quarter-car model is investigated. In this model, the damping coefficient of the car suspension is selected in a way that the resulting semiactive system approximates the performance of an active suspension system designed to produce sky-hook damping. According to this control strategy, the damping coefficient switches between two different values, leading to a piecewise linear dynamical model. For this model, the equation of motion is first presented in a general normalized form. Then, an appropriate methodology is applied for obtaining exact periodic motions for the case of forcing resulting from a road with harmonic profile. This methodology is based on employing the exact solution form within response intervals where the damping coefficient remains constant. The unknowns of the problem are then determined by imposing a set of periodicity and matching conditions. The stability analysis of the located motions is also performed by applying a method that is suitable for piecewise linear systems. Next, this analysis is applied and representative numerical results are presented in the form of response diagrams, illustrating the effect of the important system parameters. Finally, results obtained by direct integration of the equation of motion are also presented for transient road excitation. All the results are compared to those obtained for the conventional suspension systems including passive bilinear shock absorbers.