The theoretical model of shock wave attenuation in PMMA

摘要

A new analytic model of the intense shock-wave decay is deduced in the paper based on self-consistent and well-defined assumptions. The shock wave attenuation in PMMA can be divided into two stages. In the initial decay, a spherical wave model is adopted because the dimension of the wave origin is too small to be neglected in comparison with the dimension of target. Due to overdamp at initial stage, the pressure gradient along the radial direction is expressed as dp/dr-=f(rho p/rho t, du/dp) with the term (du/dp) deduced from the transient equation of wave front and the linear relation between the wave velocity and particle velocity at the wave rear. A temporal equicrural trapezoidal pressure profile applied to the target surface is used as the initial condition in order to obtain the pressure of rho p/rho t. This pressure profile induces three stages of shock wave evolution: (1) The formation stage of "pressure increase"; (2) The plateau of "maximum pressure"; (3) The decay stage of "pressure decreases". According to the relation between the surge pressure of shock wave and laser power density, the character of laser-induced shock wave is described in detail. The above assumptions could not be applied in the final stage of propagation because the distorted anegative" pressure caused by the overdamp assumption would appear. In the final stage, the famous Taylor's equations of shock wave attenuation based on underdamp assumption are adopted. The theoretical model and the numerical results are in good agreement with the experiment.