ON THE CRITICAL AMPLITUDES OF ACCELERATION WAVE TO SHOCK-WAVE TRANSITION IN WHITE-NOISE RANDOM-MEDIA

The problem of transition of acceleration waves into shock waves is ad dressed in the context of weakly random media. A class of random media is modeled by a vector white noise random process representing two ma terial coefficients appearing in the Bernoulli equation governing the evolution of acceleration waves. The problem of shock formation. which involves a stochastic competition of dissipation and elastic nonlinea rity, is treated using a diffusion formulation for the Markov process of the inverse amplitude. The first four moments of the critical inver se amplitude are derived explicitly as functions of the means and cros scorrelations of the underlying vector random process. It is found tha t the Stratonovich as well as the Ito interpretation of the stochastic Bernoulli equation lead to an increase of the average critical amplit ude of the random medium problem over the critical amplitude of the de terministic homogeneous medium problem. Probability distribution of th e critical inverse amplitude is found to be, in general, of Pearson's Type IV.