粘性介质上的悬臂梁在冲击载荷作用下的刚塑性动力响应

DYNAMIC RESPONSE OF RIGID-PLASTIC CANTILEVER BEAMS IN VISCOUS MEDIUM UNDER IMPULSIVE LOADINGS

本文考虑了一个放置在粘性介质上的刚-理想塑性悬臂梁在自由端受冲击载荷时的小变形动力响应。具体讨论了线性粘性介质时矩形脉冲,线性衰减脉冲及瞬时冲击等加载情况,并与无介质解进行了比较,讨论了介质对梁的运动变形模式、最终挠度、能量吸性的影响。

Dynamic response of rigid-perfect plastic cantilever beams resting upon viscous medium is studied. It is assumed that the reaction of the medium is a force with an intensity proportional tq the n-th power of the deflection velocity. For general end dynamic loading. it is found that there is a necessary condition for the existence of a complete solu- tion of infinitesimal deflection response. Both mode and complete solutions are found in the case of n=1. Several cases of impulsive loading (rectangular pulse, linearly reduced pulse and instantaneous pulse), which is added on the free end of the beam, are discussed in detail. The results are compared with those without medium. The effects of the medium to the kinematic deformation forms of the beam, the final end deflection, and the energy absorbed by the medium are also given.Two main conclusions of this papre are: first, the finaf end deflection of the beam in dynamic response is very sensitive to the existence of viscous medium, that is. very weak viscosity can make the deflection reducing a lot And the sensitivity is increased with the intensity of the impulsive load; the second is that although the kinematic deformation form is mainly determined by the load intensity and the shape tin which way it is applied),the viscous medium does have influences in some cases. When linearly reduced pulse is applied at the end of the beam, for example, there exists one kinematic deformation mode which is not appeared without the medium.