弹性压应力波下直杆动力失稳的机理的判据

基于应力波理论和失稳瞬间能量的转换和守恒，导出了一个直杆动力分岔失稳的准则：（1）直杆在发生分岔失稳的瞬间所释放出的压缩变形能等于屈曲所需变形能与屈曲动能之和；（2）在上述能量转换过程中，能量对时间的变化率服从守恒定律。应用临界条件（1）推导出的直杆动力失稳的控制方程和杆端边界条件以及连续条件，与应用哈密顿原理推导的结果完全相同，但不足以构成求解直杆动力失稳问题的完备定解条件，导出包含两个特征参数的一对特征方程。从而建立了求解直杆动力失稳模态和两个特征参数（临界力参数和失稳惯性项指数参数即动力特征参数）的较严密理论方法。

MECHANISM AND CRITERION FOR DYNAMIC INTABILITY OF BARS UNDER ELASTIC COMPRESSION WAVE

On the basis of transformation and conservation of energy, a criterion is presented and two critical conditions are derived for the dynamic bifurcation instability of straight bars under an axial step-load, with the stress-wave propagation taken into consideration. The first critical condition is that the amount of released compressive deformation energy must be equal to the sum of buckling deformation energy and buckling kinetic-energy at the instant when the dynamic bifurcation occurs. The second critical condition is that the rate of the energy transformation obeys the conservation law in the instant course of buckling. The governing equations, the boundary conditions and the continuity conditions derived by use of the first critical condition are the same as those obtained by use of Hamilton's theorem. Only one characteristic equation is derived by use of the above-mentioned equations and conditions, and is insufficient for determining the two characteristic parameters that are the critical load parameter and the exponential parameter of buckling inertia effect. The latter is named as the dynamic characteristic parameter in this paper. A supplementary restraint-equation at the compression-wave front is derived by use of the second critical condition. A couple of characteristic-equations for the two characteristic parameters are derived on the condition under which the governing equations have nontrivial solutions satisfying the boundary conditions, the continuity condition and the supplementary restraint-equation. The dynamic buckling modes, the critical load parameter and the dynamic characteristic parameter are obtained accurately on the basis of the solutions of the characteristic equations.