Assessing tire forces due to roadway unevenness by the pothole dynamic amplification factor method

A technique is developed to assess the dynamic contact forces arising after passing road surface irregularities by a vehicle modelled as a general linear MDOF system. The equations governing vibration of a vehicle moving along an uneven profile are, first, transformed to the state-space form and, then, to a system of uncoupled first order complex differential equations. For a local roadway irregularity described functionally, solutions of all equations are found analytically and expressed in terms of a unique function of one complex variable, the so-called pothole dynamic amplification factor, which is specific to the irregularity shape. The solutions obtained are combined to give dependencies of the harmonic components of the contact forces arising after the passage of the irregularity on the vehicle speed and irregularity dimensions. The problem is shown to be decomposed into separate calculation of vehicle and pothole-specific data. The technique developed is not specific to a particular vehicle model or an irregularity shape: the vehicle model is represented by its mass, stiffness, and damping matrices, and the replacement of one irregularity by another simply requires replacement of one dynamic amplification factor function by another. The latter are derived in Appendix A for several pothole configurations. The discussion is amply illustrated by examples of the application of the technique to the calculation of the tire forces for two simple vehicle models and several potholes of different shape.