非线性弹性介质中冲击波斜反射的研究(Ⅱ)

STUDIES ON OBLIQUE REFLECTION OF SHOCK WAVE IN NONLINEAR ELASTIC MEDIA (Ⅱ)

利用前文结果求解了冲击波在固壁及滑动刚壁两种边界面上的斜反射问题。在滑动刚壁的情,很可能出现马赫反射图象。

In a former paper, the problem of oblique reflection of shock wave in iso-tropic hyperelastic media under plane-strain condition was discussed by using small deformation theory. The constitutive equations of materials and the solutions for simple waves and shock waves were presented. An solution for oblique reflection of a pressure shock wave impinging on a free surface was given.In this paper, the constitutive equations and the solutions for simple waves and shock waves developed in the former paper are presented first, and then the oblique reflection of shock waves impinging on a rigid boundary and a lubricated-rigid boundary is studied.The reflected wave patterns are shown in Fig. 1 and Fig.2. For the mediuum we considered here. one of the reflected waves (slow wave) is always a shock wave. and the other reflected wave (fast wave) may be either a shock wave or a simple wave. In the case of rigid boundary, the reflected fast wave changes from a shock wave to a simple wave as the incident angle of the incident pressure shock wave increases. The reflected fast wave will vanish when the incident wave satisfies some certain conditions. Fig.3 shows the correspondence of the reflected wave patterns with the incident wave conditions. Fig.4 presents the results for incident shear shock waves. In this case, the reflected fast wave is a shock wave or a simple wave depending upon the sign of the incident shear shock wave. Again, for some certain incident shear shock waves, there exists only one reflected wave. In the case of lubricated-rigid boundary, a incident pressure shock wave generates only a reflected pressure shock wave, as shown in Fig.5. and a incident shear shock wave generates an identical shear shock wave. Fig.6 shows the ratio between the amplitudes of the reflected and the incident pressure shock waves. It is noticeable that when the incident angle tends to the critical angle, the amplitude of the reflected shock wave increases. we think that a Mach reflection pattern similar to that in gas dynamics is very likely to take place in irregular reflection.