修正弹性应力波的柱面波波动方程推导及数值分析
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重庆大学

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国家自然科学基金项目(面上项目,重点项目,重大项目)


Derivation and Numerical Analysis of Cylindrical Wave Equation for Correcting Elastic Stress Waves
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Chongqing University

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    摘要:

    为了研究应力波传播在工程领域的一些应用问题,以及传统应力波理论存在的缺失及不完善问题,根据修正的弹性应力波理论,通过张量分析推导建立了柱坐标系下的体积波波动方程和形变波波动方程、以及求解波动方程的初始条件和边界条件。然后对波动方程用有限差分法建立差分格式,根据差分格式使用matlab求解波动方程得到应变随时间的变化关系。应力波在空心圆柱中的时空演化传播过程就可以得出。据此从理论层面和数值解认识在柱坐标系中分析了体积波与形变波的关系,在理论中得到了几何模型对应力波传播的影响。

    Abstract:

    In order to study some application problems of stress wave propagation in engineering field and the lack and imperfection of traditional stress wave theory, according to the modified elastic stress wave theory, the volume wave equation under cylindrical coordinate system is established by tensor analysis. And the wave equation of the deformation wave, and the initial conditions and boundary conditions for solving the wave equation are also established. Then the difference equation is established by the finite difference method for the wave equation, and the strain equation is obtained by using the matlab to solve the wave equation according to the difference format. The space-time evolution propagation process of stress waves in a hollow cylinder can be obtained. Based on this, the relationship between volume wave and deformation wave is analyzed in the cylindrical coordinate system from the theoretical level and numerical solution. The influence of geometric model on stress wave propagation is also obtained in theory.

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历史
  • 收稿日期:2019-03-10
  • 最后修改日期:2019-06-25
  • 录用日期:2019-06-26
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