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三维弹性固体中冲击波传输方程的Lagrange描述

李永池 丁啟财

李永池, 丁啟财. 三维弹性固体中冲击波传输方程的Lagrange描述[J]. 应用数学和力学, 1982, 3(4): 449-462.
引用本文: 李永池, 丁啟财. 三维弹性固体中冲击波传输方程的Lagrange描述[J]. 应用数学和力学, 1982, 3(4): 449-462.
Li Yong-chi, T. C. T. Ting. Lagrangian Description of Transport Equations for Shock Waves in Three-Dimensional Elastic Solids[J]. Applied Mathematics and Mechanics, 1982, 3(4): 449-462.
Citation: Li Yong-chi, T. C. T. Ting. Lagrangian Description of Transport Equations for Shock Waves in Three-Dimensional Elastic Solids[J]. Applied Mathematics and Mechanics, 1982, 3(4): 449-462.

三维弹性固体中冲击波传输方程的Lagrange描述

Lagrangian Description of Transport Equations for Shock Waves in Three-Dimensional Elastic Solids

  • 摘要: 在Lagrange坐标中导出了三维非线性弹性固体中冲击波幅度在任意传播方向上的传输方程.导出的方程说明,冲击波的幅度在任意传播方向上随时间的变化率依赖于(i)冲击波阵面紧后方介质运动的一个未知量;(ii)冲击波阵面的两个主曲率;(iii)冲击波法向波速在阵面内的表面梯度;(iv)和冲击波前方介质运动有关的非齐次项,当前方介质处于均匀运动状态时此项为零.文中指出了适当选择传播矢量以简化传输方程的几种方法.我们还得到了一组与介质本构方程无关的、联系冲击波各跳跃量变化率的普适关系.
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    [8] Wright,T.W.,An intrinsic description of unsteady shock waves,Q.J.Mech.Appl.Math.,Vol.24,(1976),311-324.
    [9] Ting,T.C.T.,Intrinsic description of the three-dimensional shock waves in nonlinear elastic fluids.Int.J.Eng.Sci.,Vol.19,(1981),629-638.
    [10] Ting,T.C.T.and Li,Y.C.,Eulerian formulation of transport equations for three-dimensional shock waves in simple elastic solids.(submitted for publication).
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出版历程
  • 收稿日期:  1981-12-28
  • 刊出日期:  1982-08-15

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