An exact analytical solution to the problem of the wave motion of a tubular semi-infinite rod interacting with its surrounding elastic medium according to the Coulomb’s law of dry friction under the action of an exponentially falling dynamic load on its end (modeling of explosive charge detonation) and in the case of a finite mass impact by a rigid body along this end is obtained. The pattern of wave motion depending on the loading parameters is investigated: the leading and trailing edges of the elastic wave are determined, and the distribution of residual strains as it passes along the rod is found. The obtained results can be used in calculating the deformation of oil and gas pipelines in the case of shock loads.

中文翻译：

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考虑干摩擦的管道动态影响

根据库仑干摩擦定律在其端部呈指数下降的动态载荷作用下，根据管状半无限杆与其周围弹性介质相互作用的波动问题的精确解析解（爆炸装药爆轰的模型） ），并且在有限质量的情况下，刚体会沿此端受到冲击。研究了取决于载荷参数的波动模式：确定了弹性波的前缘和后缘，并找到了沿杆通过时的残余应变分布。所得结果可用于计算冲击载荷作用下油气管道的变形。