理论模型计算爆炸荷载作用下简支梁动力响应

Simply Supported Beam Explosion Response Based on Theory Models Title

摘要:

根据爆炸动力与振动力学理论采用Euler梁模型与改进的Timoshenko梁模型分别分析了简支梁的动力响应.爆炸荷载被简化为三角形荷载.爆压计算公式采用J.Henrych公式.结果表明简支梁的动力反应包含2个阶段，分别为受迫振动阶段（弹性和塑性）和自由振动阶段.建立挠度应力方程用来判断梁的屈服.通过计算分析可知，与Euler梁结果相比，有限元计算结果相对更接近于Timoshenko梁模型计算结果.这是由于修正Timoshenko梁理论中考虑了剪切惯性效应的缘故.考虑实际工程中梁支承端部的约束形式对梁受荷载作用的影响，将端部约束简化为含有弹簧与阻尼共同作用的模型，研究弹性支撑系数、弯矩抵抗系数及阻尼系数参数变化对控制位移的影响.

Abstract:

According to the explosive dynamics and vibration theory, utilized theory model of Euler beam and improved Timoshenko beam to analysis dynamic response of simply beam. Blast load was simplified to triangle load. The explosion overpressure was determined by J. Henrych. The results show that dynamic response is divided into two phases, i.e. comprising forced vibration stage (elastic and plastic) with load and free vibration stages with noload. Furthermore, beam yield judgment used equation of the relation between deflection and stress. The numerical calculations of the finite element model relatively good fitted to the theoretical values of Timoshenko beam model compared to the Euler beam model. Considering shear inertial effect in Timoshenko beam theory lead to this phenomenon. For the requirement of engineering practice, constraint form of propping end effect on beam response, constraint form is simplified to model which contains spring and damping. Through coefficients variation of elastic propping, resistance moment and damping to research variation of critical displacement.