闭口薄壁杆件受碰撞的振动方程求解

Solution of Dynamic Equation in Thin-Walled Close Section Beam under Impact

基于薄壁杆件理论、能量泛函变分原理和闭口薄壁杆件翘曲函数的特征,推导了闭口薄壁杆件的双向弯扭耦合动力方程,此方程可退化为Bernoulli-Euler梁弯扭耦合动力方程.根据结构的边界条件、连续条件和碰撞接触平衡条件,采用Laplace积分变换和逆变换方法求解闭口薄壁杆件受碰撞的动力方程,获得了闭口薄壁杆件的各种瞬态动力响应.将结果与Bernoulii-Eurler薄壁梁理论结果相比较,计算结果表明:考虑剪切变形对冲击力和扭转角的影响不大,但对位移的影响比较显著.

The dynamic differential equations of coupled bending and torsional vibration in Timoshenko thin-walled beam with closed section had been deduced based on the theory of thin-walled structures,the dynamic differential equations and the characteristic of warping function.The equations can be degenerated into the differential equation of coupled bending and torsional vibration in Bernoulli-Euler thin-walled beam with closed section.Then,according to boundary conditions,continuous condition and impact contact equilibrium condition,the dynamic differential equations in thin-walled closed section beam under impact were solved by Laplace transform and inverse transform,and all kinds of transient dynamic responses of beam have been obtained.Finally,the result was compared with the result which was solved based on the theory of BernoulliEuler thin-walled beams.It shows that shear deformation has little effect on impact force and torsion angle,but has much effect on displacement.