矩形板中应力波主波和次波的传播与反射

Propagation and reflection of stress wave about primary and secondary waves in rectangular plates

弹性应力波的修正理论指出关于体积应变的波动方程与现有理论一致,但发展了一组关于体积应变和偏应变的弱耦合波动方程。针对矩形板受侧向集中载荷冲击下应力波的波动问题,建立了应力波传播的两组控制方程以及加载面和自由面的波动边界条件。采用有限差分方法求解波动方程,数值分析了应力波关于主波和次波的传播以及自由面上斜入射波的反射过程。偏应变在传播过程中分裂为两部分,一部分与体积应变共同传播组成主波,另一部分传播较慢形成次波。数值模拟结果显示与冲击载荷下纳钙玻璃板中应力波的传播图像是完全符合的。

The modified theory of elastic stress waves asserts that the wave equations governing volume strain are consistent with existing theories,but a new set of weakly coupled wave equations encompassing both volume strain and partial strain has been developed.To address the problem of stress wave fluctuation caused by a concentrated load impact on a rectangular plate,two sets of control equations for stress wave propagation as well as the fluctuation boundary conditions of loading surface and free surface are established in this paper.The finite difference method is used to solve the wave equation,and the stress wave is simulated numerically for the propagation of the main and secondary waves and the reflection process of oblique incident waves on the free plane.During propagation,the partial strain splits into two parts:one part propagates together with the volume strain,forming the main wave,while the other part propagates at a slower pace,resulting in the formation of a secondary wave.The numerical simulation results show complete consistency with regard to the propagation image of the stress waves in the nanocalcium glass plate under shock loading.