Vibration Analysis of Multiple Parallel Timoshenko Beams with Intermediate Flexible Connections subjected to a Moving Mass

In this article, the vibration analysis of parallel Timoshenko beams connected by flexible connections is studied in which a moving mass passes from one or a number of the beams. In this system, the number of beams and flexible connections is arbitrary. The moving mass is considered to travel with a constant velocity or acceleration. All forces between the beam and the moving mass are considered such as gravity, coriolis, centrifugal, inertia and mass acceleration. The method involves a change of variables and modal analysis to decouple and to solve the governing differential equations, respectively. The eigenvalues and eigenfunctions of the system are obtained adopting transfer matrix method, andthe method of auxiliary functions is applied to separate the coupled second order differential equations. The displacements and the bending moments of the system subjected to the moving mass will be examined. The moving force formulation can be achieved by considering only the gravitational force. The system response by considering the moving mass is obtained and compared with the moving force problem and the effects of the inertia, coriolis, centrifugal and mass acceleration, is investigated, separately.