A novel approach to the calculation of pothole-induced contact forces in MDOF vehicle models

A technique is developed to predict the dynamic contact forces arising after passing road surface irregularities by a vehicle modelled as an undamped multiple-degrees-of-freedom (MDOF) system. An MDOF system moving along an uneven profile is decomposed into an aggregate of independent oscillators in the modal space, such that the response of each oscillator can be calculated independently. An equation relating the contact forces in the physical space to the modal forces is established. The technique developed is applied to the calculation of the coefficients of the harmonic components of the contact forces arising after the passage of a “cosine” pothole. The application of the technique to various problems, such as evaluation of the effect of parameter modifications on the vehicle dynamics and reduction of vehicle models in bridge-related problems, as well as its extension to the damped case, are also discussed. One interesting phenomenon reported in the DIVINE project [1], regarding the replacement of a steel suspension by an air suspension, resulting in an increase of the maximum response of short-span bridges, is explained by applying the technique suggested. The discussion is amply illustrated by examples of the application of the technique to the calculation of the tire forces due to a pothole for two simple—quarter-car and half-car—vehicle models.