Dynamic response of bending-torsion coupled beam under elastic impact

For a moving rigid-body impacting on a cantilever end, based on bending-torsion coupled dynamic model of Timoshenko beam, the rigid-body and the beam are regarded as an integrated system of vibration. The general solutions are supposed, and the frequency equation, mode shape and lumped mass of the impact system are yielded. Then the dynamic response is expressed in Duhamel integration where the unknown parameters are determined by the initial impact conditions. Thus the results of dynamic response and impact force are presented with direct mode shape superposition method (DMSM). The numerical results of the impact force are presented and discussed for three beams: bending-torsion coupled beam, bending-torsion beam with little coupling stiffness and Timoshenko isotropy beam without torsion effect. It is concluded that the bending-torsion coupled composite beam impact force can be decreased much more than that of the isotropy Timoshenko beam under the same condition.