Quasitransverse shock waves in elastic media with an internal structure

Journal of Applied Mechanics and Technical Physics - Tập 40 - Trang 341-346 - 1999
N. I. Gvozdovskaya, A. G. Kulikovskii

Tóm tắt

We consider the structure of small-amplitude quasitransverse shock waves in a weakly anisotropic elastic medium which possesses an internal structure generating the wave dispersion. The dispersion is modeled by introducing terms with higher derivatives into the equations of the theory of elasticity, and the dissipation is represented by viscous terms. In one of the two possible cases treated below, the requirement that the discontinuity structure exist leads to a set of admissible discontinuities of complex structure. A considerable part of the shock adiabat consists of a set of short portions and separate points, the number of which increases as the viscosity decreases. This complex set of admissible discontinuities is the general case where the dispersion in the shock-wave structure is sufficiently strong.

Tài liệu tham khảo

N. S. Bakhvalov and M. E. Églit, “Variational properties of the averaged models of periodic media,”Tr. MIAN,192, 5–19 (1990). A. G. Kulikovskii and N. I. Gvozdovskaya, “The effect of dispersion on a set of admissible discontinuities in continuum mechanics,”Tr. MIAN,225, 73–85 (1998). A. G. Kulikovskii and E. I. Sveshnikova,Nonlinear Waves in Elastic Media [in Russian], Mosk. Litsei, Moscow (1998). N. I. Gvozdovskaya and A. G. Kulikovskii, “Electromagnetic waves and their structure in anisotropic ferromagnetics,”Prikl. Mat. Mekh.,61, No. 1, 139–148 (1997). A. G. Kulikovskii and E. I. Sveshnikova, “Structure of quasitransverse shock waves,”Prikl. Mat. Mekh.,51, 926–932 (1997). L. D. Landau and E. M. Livshits,Theoretical Physics, Vol. 6:Hydrodynamics [in Russian], Nauka, Moscow (1986).