弹性基础上封闭型梁的等效刚度及其动态响应

Equivalent Stiffness and Dynamic Response of a Circular Beam on Elastic Foundation

从柔性耗能防撞装置出发,建立一个弹性基础上封闭型梁的分析模型,该模型由分布的辐射弹簧和与弹簧连接的两个同心圆环组成。利用曲梁理论和弹性基础梁理论,分别建立外钢围圆环在静态集中力作用和动态冲击载荷作用下描述外钢围径向位移的控制方程。针对外钢围承受静态集中力载荷情况,通过特定边界条件获得径向位移的精确解,推导得到防撞装置的等效刚度;针对外钢围承受动态冲击载荷情况,通过特定边界条件和初始条件,形成完全的初边值问题,应用Laplace变换和Laplace数值反变换技术对该初边值问题进行求解,得到外钢围在受冲击载荷作用下的动态响应。

Based on the design of flexible crashworthy structure,an analytical model was established for a circular beam on elastic foundation.The model was composed of an outer circular beam connected to the inner circular bridge pile through distributed springs.The governing equations for the radial displacement of the outer beam were deduced for the beam under a concentrated force or a dynamic impact load.With adequate boundary conditions,the equivalent elastic stiffness of the structure was obtained from the quasistatic solution for the outer beam under concentrated force.Governing equation deduced for the outer beam under dynamic impact force,together with adequate boundary conditions and initial conditions,form an initial-boundary value problem（IBVP）.This IBVP was solved by the method of Laplace transform and the numerical inverse Laplace transform to get the dynamic response of the outer beam.