摘要
基于冲击力学基本理论,研究了刚塑性自由梁在偏心阶跃荷载下的动态响应。根据动平衡条件和梁的变形模式,推导了不同荷载水平下无约束自由梁的加速度和角加速度公式。通过动静法得到了自由梁内的弯矩和剪力,依此给出了塑性铰的位置,得出了不同荷载位置下塑性铰的临界荷载值,并讨论了摩擦力对其的影响。结果表明:摩擦力较小时,其对塑性铰的位置有明显影响;但摩擦力较大时,塑性铰的位置几乎不随摩擦力的变化而改变,并且出现塑性铰的临界荷载很小。在荷载水平较低时,自由梁只可能在荷载作用点产生塑性铰;随着荷载水平的提高,在长梁段会出现一个与荷载作用点塑性铰相反的塑性铰;当荷载很大时,在短梁段也会出现一个塑性铰。此外,荷载作用点的位置对塑性铰临界荷载值也有较大影响,荷载离梁端越近,塑性铰临界荷载值越大;若荷载离梁端越远,塑性铰临界荷载较小。
According to the basic theory of impact dynamics, the dynamic responses of rigid-plastic free beam under eccentric load step are studied in this paper. The formulas of accelerations and angle accelerations of the unconstrained free-free beam under different load levels are derived by means of the dynamic balance condition and the deformation model of the beam. The bending moment and the shear force in the free beam are obtained in considering the influence of inertia force. The location of the plastic hinge and the critical load value of the plastic hinge under different load location are given. The influences of frictional force are discussed. It is shown from the calculating results that the friction force has obvious influence on the position of plastic hinge in the lower friction force. But in the case of large friction, the position of the plastic hinge is hardly changed with the change of friction, and the critical load of the plastic hinge is very small. If the load level values are very small, the plastic hinge in the free beam can only be produced at the load point. With the increase of load level, the plastic hinge opposite to the plastic hinge at the load point will appear in the long beam segment. A plastic hinge also appears in the short beam segment when the load is very large. In addition, the positions of load points have great influences on the critical load of plastic hinge. The closer the load is to the beam end, the greater the critical load of the plastic hinge is, and vice versa.
出处
《应用力学学报》
CAS
CSCD
北大核心
2018年第5期1002-1007,共6页
Chinese Journal of Applied Mechanics
基金
国家自然科学基金(50978058)
广东省自然科学基金(S2011010005037)
关键词
刚塑性
自由梁
偏心荷载
摩擦力
动态响应
rigid-plastics
free-free beam
eccentric load
frictional force
dynamic response
