Ondes de Choc Finies Dans les Solides Elastiques

Interaction of a characteristic shock with a weak discontinuity in a relaxing gas

“…For a characteristic shock, this acceleration is not an unknown, and the amplitudes of the reflected and transmitted waves can be completely determined. It is shown in [20] that the general theory for problems of wave interaction, which originated from the work of Jeffrey [21], leads to the results obtained by Brun [22] and Boillat and Ruggeri [23]; the theory has been successfully used for different material media (see [24][25][26]). In order to study the nature of amplitudes of the reflected and transmitted weak discontinuities, we consider the Interaction of a weak discontinuity with a characteristic shock giving rise to reflected and transmitted waves generalized conservation systems that are direct consequences of the original system (1), and have the following forms in the regions behind and ahead of the shock (i.e., to the left and to the right of the discontinuity, which propagates with the speed V = u):…”

Group theoretic method for analyzing interaction of a discontinuity wave with a strong shock in an ideal gas

“…This, in effect, asserts that when the incident wave with velocity λ (1) at t = t p encounters the shock wave, it gives rise to two reflected waves with velocities λ (2) and λ (3) in the shock acceleration |[V ]| at the collision time t = t p can be determined from the algebraic system of equations…”

“…The coefficients α and β determine the amplitude vectors Λ 2 = αd (2) (t p ) and Λ 3 = βd (3) (t p ) of the reflected waves propagating along the shock fronts with velocities λ (2) and λ (3) , respectively. Moreover, an increase in the magnitude of the initial discontinuity π 0 associated with the incident wave, cause the amplitudes α, β and the shock acceleration to increase in magnitude.…”

“…They form an important class of solution of nonlinear hyperbolic systems. A detailed study towards gaining a better understanding of the wave interaction problem within the context of hyperbolic system has been carried out by Jeffrey [1], Brun [2] and Morro [3,4]. A further contributions to the study of characteristic shocks (see, Boillat and Ruggeri [5]) and wave interactions which enable the evaluation of reflected and transmitted wave amplitudes when the discontinuity wave encounters a characteristic shock may be found in the paper of Boillat and Ruggeri [6].…”

“…The application of this work, to interaction with a shock, has been carried out by Ruggeri [7], Virgopia and Ferraioli [8], Radha et al [9], Pandey and Sharma [10], Pandey et al [11] and Mentrelli et al [12], in various fields. It is a known fact that the shock undergoes an acceleration jump as a consequence of an interaction with the a weak wave; this fact was accounted for in the work of Brun [2] and Boillat and Ruggeri [6].…”