弹性撞击作用下弯扭耦合梁的动力响应

Dynamic Response of Bending-torsion coupled Beam under Elastic Impact

对于质量块以一定初速度撞击悬臂梁端部问题,基于弯扭耦合Timoshenko梁模型,把质量块与悬臂梁作为一个整体振动,动力响应以Duhamel积分表示,使用模态叠加法给出动力响应与撞击力的结果。对于悬臂梁受质量块撞击的算例,分别分析了弯扭耦合梁、弯扭耦合系数很小的梁和各向同性Timoshenko梁,对比讨论了撞击力结果。

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.