The interaction dynamics of a vehicle traveling along a simply supported beam under variable velocity condition

Abstract

This paper studies the interaction dynamics of a vehicle traveling on a simply supported beam. A simple quarter-car planar model of the vehicle is taken into account. The system of the quarter-car model is treated as a moving mass with a massless harmonic force rolling on a simply supported beam. The objective of this paper is to present analytical and numerical methodologies to evaluate the vehicle–beam coupling effects when the vehicle moves under variable speed condition. Due to the presence of friction and convective acceleration, the vehicle can be accelerated by a forward force. Meanwhile, the vehicle is capable of reducing speed by applying a retard force to the vehicle and/or increasing the friction between the vehicle and beam. This results in variable velocity, acceleration, and deceleration, as well as unknown location of the vehicle along the beam. Result shows that as the spring stiffness of the suspension is close to the resonant value, strong commensurability between the oscillating frequency of the vehicle and the vibrant frequency of beam occurs when the instantaneous speed of the vehicle becomes a small quantity. In other words, a commensurable condition between the vehicle and beam is weakened when the vehicle is accelerated by a positive driving force; it becomes strong if the vehicle is decelerated by a negative reverse force and friction. If the vehicle reduces its traveling speed sharply, large amplitude and high oscillating frequency of the vehicle were generated. This significantly reduces the riding comfort for passengers in the vehicle. The applied force and coefficient of friction can be treated as tuning parameters to determine the resonant region of the interaction dynamics of a vehicle–beam system.