Simulation of stress wave diffraction by various obstacles in a continuous medium

Abstract

The diffraction of elastic waves by various obstacles (cavities, cylindrical linings, solid inclusions) in continuous media is of marked theoretical and practical interest. When tunnels are driven by blasting, one is faced with the necessity of investigating the dynamic reaction of hydraulic engineering, transport, and other tunnels during their interaction with the shock wave.s.The difficulties of theoretical approaches [1-3] to such problems make it necessary to use experimental procedures, for example in studying the dynamic stress concentration at obstacles of various characters and forms. Such problems are simulated [4][5][6] by the method of dynamic photoelasticity [7,8], which enables one to observe and record the diffraction wave stress fields which arise in the vicinity of the obstacle throughout the period of interaction. Using the dynamic photoelasticity method, we have investigated the following problem experimentally. A direct compression wave (P wave) strikes an obstacle and begins to interact with it at a fixed moment of time t= 0. We examined three alternative types (in terms of boundary conditions) of circular cylindrical obstacles ( A complete solution to the problem of dynamic stress concentration presupposes an investigation of the effects of all its governing parameters throughout the practically important range as far as establishment of self-similar regions of change of their numerical values. In the case of a plane-wave approximation of the solution, the parameters R/r and r/X, respectively characterizing the curvature of the incident wave front and the relative distance from the source of perturbation, are eliminated from the analysis. Thus the governing parameters of the solution of (1) reflect the geometrical and physical aspects of this problem as well as the dimensionless time of the diffraction process.For these types of obstacles (see Fig. 1), (1) breaks down into three particular cases: