Abstract—

In this paper, asymmetric equations for an elliptical boundary layer in the vicinity of the conditional front of Rayleigh surface waves, which occurs in shells of revolution under shock end impacts of normal type are constructed. The technique of asymptotic derivation of these equations, based on the use of the symbolic Lurie method and the introduction of special coordinates that distinguish a small frontal zone required to reduce the original problem to an equivalent problem for an infinite shell by isolating a particular solution. The considered boundary layer complements the full description of the considered type of stress-strain state (SSS) in all sections of the phase plane. It also uses a quasi-static boundary layer of the Saint-Venant type in a small vicinity of the butt end, a parabolic boundary layer according to the two-dimensional Kirchhoff–Love theory, a quasi-plane short-wave component, and a hyperbolic boundary layer in a small neighborhood of the shear wave front. In conclusion, an example of constructing an elliptical boundary layer under shock action on the butt end of a cylindrical shell is considered.

中文翻译：

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法向冲击载荷作用下旋转壳椭圆边界层的渐近研究

摘要-

在本文中，构造了在正常类型的冲击端冲击下旋转壳中出现的瑞利面波的条件前沿附近的椭圆边界层的不对称方程。这些方程的渐近推导技术是基于符号Lurie方法的使用和特殊坐标的引入而进行的，这些特殊坐标区分了一个较小的额叶区域，该区域需要通过隔离特定解来将原始问题简化为无限壳体的等效问题。所考虑的边界层是对相平面所有部分中所考虑的应力应变状态（SSS）类型的完整描述的补充。它还在对接端的一小部分附近使用了Saint-Venant类型的准静态边界层，根据二维Kirchhoff-Love理论的抛物线边界层，准平面短波分量和剪切波前的小邻域中的双曲边界层。总之，考虑了在圆柱壳的对接端受冲击作用下构造椭圆形边界层的示例。