Theoretical Formulation of Three-Mass Vehicle Model for Vehicle–Bridge Interaction

The vehicle–bridge interaction (VBI) is studied using a semi-analytical approach based on a three-mass vehicle model. As most work analyzes vehicle–bridge interaction numerically and/or analytically by treating the vehicle as a simplified lumped mass, to the best of the author’s knowledge, this work first presents the theoretical formulation of the three-mass VBI system, where a more realistic vehicle model equipped with a rigid mass and two unsprung mass-spring-damper systems is considered. By assuming the first modal vibration of beam, the semi-analytical solutions are derived, which can be served as the reference solutions for calibrating VBI analyses using different models or methods.