应力波传播与屈曲耦合情况下结构动力屈曲控制方程及波前边界条件的探讨

DERIVATION OF GOVERNING EQUATIONS FOR DYNAMIC BUCKLING OF STRUCTURES UNDER COUPLED STRESS WAVE PROPAGATING AND DYNAMIC BUCKLING

从应力波作用下结构动力屈曲的特点出发,指出应力波作用下结构屈曲与应力波传播的耦合导致时间成为结构屈曲的参变量,从而应力波作用下结构屈曲的真实运动与邻近运动是不同时刻、不同扰动区域的比较,这使得其控制方程的建立不宜采用传统的等时积分变分原理;以压应力波作用下弹性直杆为例,应用能量守恒原理,根据屈曲时刻结构能量的转换关系,建立了其屈曲控制方程,并实际推导得到了波前边界条件为横向位移,转角和曲率为零;其中,波前边界第三个条件出现的原因是轴向应力波的传播与屈曲的耦合.

Because of the coupling of dynamic buckling and stress wave propagating, the traveling time of the stress wave becomes one of the parameters in dynamic buckling caused by stress waves. So the real displacement and the adjacent displacement of the dynamic buckling caused by stress waves occur at differ- ent time and different area, which make it unsuitable for using of the integral variational principle in deriva- tion of governing equations for dynamic buckling of structure under compression wave. Take the elastic col- umn as an example, by use of the conservation law of energy transformation in the instant course of buck- ling, the governing equations of column under elastic compression wave is derived. Results show that lateral displacement, rotation angle and curvature at the compression-wave front should equal to zero, and the ap- pearance of the third boundary condition at the compression-wave front is attributed to the coupling of stress wave propagating and dynamic buckling.