柔性动边界梁在横向撞击下的动力响应

Dynamic responses of beams with flexible supports subject to transversal impact

研究特定约束条件下梁受横向撞击的动力响应,这些约束表现为弹性支承刚度和阻尼特征,也就是具有柔性动边界。建立了具有动边界梁的力学模型,综合考虑弹性和阻尼支承、集中质量块以及支承不对称等情况。根据撞击局部区域的接触力—嵌入深度关系式,利用拉格朗日方法建立了横向撞击下柔性动边界梁的动力方程,并通过与简支梁在相同撞击条件下撞击力、横向位移的对比分析,说明了柔性支承对结构动力响应的影响。结果表明,低速撞击条件下,柔性支承对撞击力的影响较小,但对结构位移响应的影响较显著,并且弹性支承会使梁受撞击后的变形过程与简支梁相比增加一个变形阶段。

A method for dynamic responses of beams was presented with specific constrained condition which appears as elastic and damping feature, i.e. beams with flexible supports. The mechanics models of beams with flexible supports were established, and elastic and dumping supports, lumped masses at the beams ends and non-symmetric supports were taken account. Based on the formulae of the relationship between the contact force and the embedding depth, the dynamic equations of beams with flexible supports subject to transversal impact were proposed by use of Lagrange method. The impact force and transversal displacement of the beam with flexible supports were compared with those of simply supported one under the same impact conditions, which proves the influence of the flexible supports on dynamic responses. The results show that flexible supports have little influence on impact forces but have notable influence on responses of displacement. Compared with simply supported beam, a transformation stage of the beam with elastic supports under impact was added.