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Propagation of an acceleration wave in layers of isotropic solids at finite temperatures. (English) Zbl 1231.74090
Summary: The propagation of an acceleration wave in a layered solid which consists of different isotropic solids in contact with one another is studied in the case of plane symmetry. Each isotropic solid is at a finite temperature. The amplitudes of transmitted and reflected waves in each layer are determined and the critical time when the incident wave breaks down is discussed. As an illustrative example, an acceleration wave in a semi-infinite solid embedded with a thin layer is analyzed and discussed in detail.

MSC:
74F05 Thermal effects in solid mechanics
74J30 Nonlinear waves in solid mechanics
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[1] Sugiyama, M.; Goto, K., Statistical-thermodynamic study of non-equilibrium phenomena in three-dimensional anharmonic crystal lattices. I. microscopic basic equations, J. phys. soc. jpn., 72, 545-550, (2003) · Zbl 1122.82316
[2] Sugiyama, M., Statistical-thermodynamic study of non-equilibrium phenomena in three-dimensional anharmonic crystal lattices. II. continuum approximation of the basic equations, J. phys. soc. jpn., 72, 1989-1994, (2003) · Zbl 1112.82317
[3] Sugiyama, M.; Goto, K.; Takada, K.; Valenti, G.; Currò, C., Statistical-thermodynamic study of non-equilibrium phenomena in three-dimensional anharmonic crystal lattices. III. linear waves, J. phys. soc. jpn., 72, 3132-3141, (2003) · Zbl 1072.82529
[4] G. Valenti, C. Currò, M. Sugiyama, Wave features for a new continuum model of isotropic solids, in: Proceedings WASCOM 2003, Villasimius, 1-7 June 2003, Word Scientific, Singapore, 2003, pp. 547-554.
[5] Valenti, G.; Currò, C.; Sugiyama, M., Acceleration waves analyzed by a new continuum model of solids incorporating microscopic thermal vibrations, Continuum mech. thermodyn., 16, 185-198, (2004) · Zbl 1107.74317
[6] Currò, C.; Sugiyama, M.; Suzumura, H.; Valenti, G., Weak shock waves in isotropic solids at finite temperatures up to the melting point, Continuum mech. thermodyn., 18, 395-409, (2007) · Zbl 1160.74370
[7] Sugiyama, M.; Chaki, M., Reflection and refraction of elastic waves in solids at finite temperatures up to melting point, Jpn. J. appl. phys., 44, 6B, (2005)
[8] A. Jeffrey, Quasilinear hyperbolic systems and waves, Pitman Research Note, vol. 5, London, 1976. · Zbl 0322.35060
[9] Donato, A., The propagation of weak discontinuities in quasi-linear hyperbolic systems when a characteristic shock occurs, Proc. roy. soc. edinburg, 78A, 285-290, (1978) · Zbl 0378.35045
[10] Donato, A., On a magneto-elastic system with discontinuous coefficients and the propagation of a weak discontinuities, Meccanica, 12, 127-133, (1977) · Zbl 0393.73114
[11] Brun, L., Ondes de choc finies dans LES solides é lastiques, ()
[12] Boillat, G.; Ruggeri, T., Reflection and transmission of discontinuity waves through a shock wave. general theory including also the case of characteristic shock, Proc. roy. soc. edinburg, 83A, 17-24, (1979) · Zbl 0416.76029
[13] Ruggeri, T., Interaction between a discontinuity wave and a shock wave: critical time for the fastest transmitted wave, example of the polytropic fluid, Appl. anal., 11, 103-122, (1980) · Zbl 0482.76062
[14] Morro, A., Interaction of waves with shocks in magnetofluiddynamics, Acta mech., 35, 197-213, (1980) · Zbl 0478.76127
[15] Conforto, F., Interaction between a weak discontinuities and shocks in a dusty gas, J. math. anal. appl., 253, 459-472, (2001) · Zbl 0970.76101
[16] Pandej, M.; Sharma, V.D., Interaction of a characteristic shock with a weak discontinuity in a non-ideal gas, Wave motion, 44, 346-354, (2007) · Zbl 1231.76132
[17] Mentrelli, A.; Ruggeri, T.; Sugiyama, M.; Zhao, N., Interaction between a shock and an acceleration wave in a perfect gas for increasing shock strength, Wave motion, 45, 4, 498-517, (2008) · Zbl 1231.76130
[18] Boillat, G., La propagation des ondes, (1975), Gauthier Villars Paris · Zbl 0151.45104
[19] Boillat, G.; Ruggeri, T., On the evolution law discontinuities for hyperbolic quasi-linear systems, Wave motion, 1, 2, 149-152, (1979) · Zbl 0418.35065
[20] Courant, R.; Hilbert, D., Methods of mathematical physics II, (1962), Interscience New York · Zbl 0729.35001
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