变截面悬臂空心圆柱的冲击动力特性

变截面悬臂空心柱是一类在工程中有着广泛应用的特殊结构。为了研究其在冲击荷载作用下的动力特性，通过准静态极限分析与冲击动力学理论，对其在等厚度与变厚度两种情形下的冲击响应展开研究。定义了荷载位置参数与塑性铰位置参数，并根据荷载位置参数给出了塑性铰位置的判定条件。利用动量定理与动量矩定理推导了悬臂端加速度的表达式以及塑性铰位置参数的控制方程。根据分布惯性力与剪力的微分关系以及剪力与弯矩的微分关系分别推导了剪力和弯矩的表达式；分析了荷载位置参数对塑性铰位置参数与悬臂端加速度的影响，以及塑性铰位置参数对悬臂端加速度的影响。算例结果表明：悬臂端加速度与塑性铰位置参数的本文解与数值解吻合良好；塑性铰位置参数随荷载位置参数的增大而增大，且二者关系几乎呈线性；悬臂端加速度随荷载位置参数、塑性铰位置参数的增大而减小。可见当冲击荷载明显超过固定端的静态极限荷载，且荷载位置参数小于临界荷载位置参数时，变截面悬壁空心柱将在柱中产生塑性铰。因此，出于结构可靠性考虑，工程中应对此类问题予以重视。

Impact Dynamic Characteristics of Cantilever Hollow Cylinder with Variable Cross-section

A cantilever hollow cylinder with variable cross-section is a special structure widely used in engineering. In order to study its dynamic characteristics under impact load, based on quasi-static limit analysis and impact dynamics theory, impact responses of cylinders with constant thickness and variable thickness ,were studied respectively. Load position parameter and plastic hinge position parameter are defined, and conditions for determining position of plastic hinge are derived from load position parameter. Expression of acceleration of cantilever end and control equation of plastic hinge position parameter is derived from momentum theorem and moment of momentum theorem. According to differential relationship between distributed inertial force and shear force and differential relationship between shear force and bending moment, expressions of shear force and bending moment are derived. Effects of load position parameter on plastic hinge position parameter and on acceleration of cantilever end, and effect of plastic hinge position parameter on acceleration of cantilever end were analyzed, respectively. Results of calculation examples show that paper solution of acceleration of cantilever end and plastic hinge position parameter are in good agreement with numerical solution. Plastic hinge position parameter increases with the increase of load position parameter, and the relationship between the two is almost linear. Acceleration of cantilever end decreases with the increase of load position parameter and plastic hinge position parameter. When impact load obviously exceeds static limit load of fixed end, and load position parameter is less than critical load position parameter, it can be seen that a plastic hinge is produced in cantilever. Therefore, for the purpose of the reliability of structure, attention should be paid to such problems in engineering.