Transverse vibration of a multiple-Timoshenko beam system with intermediate elastic connections due to a moving load

Based on Timoshenko beam theory, the dynamic response of an elastically connected multiple-beam system is investigated. The identical prismatic beams are assumed to be parallel and connected by a finite number of springs. Assuming n parallel Timoshenko beams, the motion of the system is described by a coupled set of 2n partial differential equations. The method involves a change of variables and modal analysis to decouple and to solve the governing differential equations, respectively. A case study is solved in detail to demonstrate the methodology and several plots of the midpoint deflections of beams are given and investigated for different values of moving load velocity and the stiffness of elastic connections. From the numerical results it is observed that the maximum deflection of the multiple Timoshenko beam system is always smaller than one of a single beam.