Vibration Analysis of an Elastic Beam Subjected to a Moving Beam with Flexible Connections

The vibration problem of a simply supported beam subjected to a moving elastic structure is investigated. The model consists of two Euler-Bernoulli beams which are assumed to be connected by flexible springs at two discrete points. The dynamic response of the simply supported beam subjected to the moving elastic beam at a constant speed is studied by the modal superposition method. The elastic stiffness and the inertial effect of the moving beam are included in the analysis. By solving the ordinary differential equations governing the motion of the model, some approximate analytical results are derived and influence factors on the dynamic response of the simply supported beam are discussed in details, including the stiffness ratio, which is defined as the stiffness of the moving beam to that of the simply supported beam, the moving velocity and the connection spring stiffness between the two beams. Results of the study imply that the connection stiffness has an apparent influence on the dynamic behavior of the simply supported beam.