质点与Euler-Bernoulli梁任意点撞击问题的解析解

ANALYTICAL SOLUTION TO IMPACT BETWEEN A PARTICLE AND AN EULER-BERNOULLI BEAM AT ARBITRARY POSITON ON THE BEAM

研究梁结构受质点横向弹性碰撞问题,把碰撞问题看成系统振动问题,并用直接模态叠加法(DMSM)求解。撞击点位于梁上任意位置,分别假设梁的左右两部分的挠度函数,根据初始条件、连续性条件和边界条件得到系统对应的频率方程,然后由杜哈梅(Duhamel)积分获得简支梁受横向碰撞时的解析解。算例讨论撞击力、挠度和弯矩的收敛性,也给出这些量随时间变化的曲线。结果显示DMSM方法的有效性并能够进一步推广。

The transverse impact between a particle and a simply supported beam is investigated.The direct mode superposition method(DMSM) is used to solve this initial value problem of the whole system.The impact point is located at arbitrary position on the beam.Supposing the deflection functions of the two parts of the beam separated by the impact point,the frequency equation of the whole system is established according to the initial condition,the continuity condition and the boundary condition.Then,using Duhamel integration the analytical solution is obtained to the beam impacted by the particle.With a numerical example,the convergence of the variables,such as,the impact force,deflection and moment is discussed.Curves of these variables varying with time are presented.The results show the effectiveness of the DMSM method.