Abstract—

An exact analytical solution to the problem of dynamic expansion of a spherical cavity in an elastic medium (soil) with an arbitrary constant speed is obtained. It is assumed that this speed can be large, up to the velocity of propagation of bulk waves in the medium, and therefore the boundary conditions must be set on the moving boundary. The found solution makes it possible to judge the impact (or control the impact) of underground explosions on objects in the “far” zone, at distances significantly exceeding the size of the cavity. Fixed incorrectness in the approximate solution of this problem, given by J. Achenbach and S. Sun. It is found that the approximate solution obtained by the Horn method, which requires a large parameter in the problem, is not valid in some regions of variation of the Poisson’s ratio of the medium and the rate of expansion of the cavity. It is shown that for those values of the indicated parameters at which an approximate solution can be taken, it agrees with the exact solution.

中文翻译：

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地下爆炸作用：弹性介质中球形空腔的快速膨胀

摘要-

获得了弹性介质（土壤）中球腔在任意恒定速度下动态膨胀问题的精确解析解。假设该速度可以很大，达到介质中体波的传播速度，因此必须在移动边界上设置边界条件。找到的解决方案可以判断地下爆炸对“远”区物体的影响（或控制影响），距离远超过空腔的大小。修正了 J. Achenbach 和 S. Sun 给出的这个问题的近似解中的错误。发现问题中需要大参数的Horn法得到的近似解，在介质泊松比和空腔膨胀率变化的某些区域中无效。结果表明，对于那些可以采用近似解的指示参数值，它与精确解一致。