A methodology is presented for optimizing the suspension damping and stiffness parameters of nonlinear quarter-car models subjected to random road excitation. The investigation starts with car models involving passive damping with constant or dual-rate characteristics. Then, we also examine car models where the damping coefficient of the suspension is selected so that the resulting system approximates the performance of an active suspension system with sky-hook damping. For the models with semi-active or passive dual-rate dampers, the value of the equivalent suspension damping coefficient is a function of the relative velocity of the sprung mass with respect to the wheel subsystem. As a consequence, the resulting equations of motion are strongly nonlinear. For these models, appropriate methodologies are first employed for obtaining the second moment characteristics of motions resulting from roads with a random profile. This information is next utilized in the definition of a vehicle performance index, which is optimized to yield representative numerical results for the most important suspension parameters. Special attention is paid to investigating the effect of road quality as well as on examining effects related to wheel hop. Finally, a critical comparison is performed between the results obtained for vehicles with passive linear or bilinear suspension dampers and those obtained for cars with semi-active shock absorbers.

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