Dynamic responses of an elastic beam moving over a simple beam using modal superposition method

The dynamic responses of an elastic beam moving over a simple beam are investigated. The elastic beam is modeled as an Euler beam with both ends free, and connected to the simple beam by two spring units. With modal superposition method, the dynamic responses of these two beams are studied. The vibrations of the simple beam are almost the same due to the moving elastic beam and rigid beam, even the latter beam ignores the flexural vibration of the elastic beam. However, the acceleration of the moving elastic beam is much larger than that of the moving rigid beam, which can be attributed to the flexible vibration of the elastic beam. With various flexural stiffness of the elastic beam, the max accelerations of the elastic beam at midpoint are computed along with different moving velocities. It is observed that, with an increase of flexural stiffness of the elastic beam, the max acceleration of the elastic beam decreases evidently.