The governing equations for a rotating monoclinic magnetothermoelastic medium are formulated in the context of the Lord–Shulman theory and are solved to yield the velocity equation that points to the existence of three quasiplane waves. Some particular cases are obtained, i.e., waves in the absence of anisotropy, rotation, and thermal and magnetic fields. A procedure for computing the angles of reflection is carried out. A numerical example is considered to show the dependence of the speeds of various plane waves on the angle of incidence, angle of reflection, rotation rate, and magnetic field strength.
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References
M. A. Biot, Thermoelasticity and irreversible thermodynamics, J. Appl. Phys., 27, 249–253 (1956).
H. W. Lord and Y. Shulman, A generalized dynamical theory of thermo-elasticity, J. Mech. Phys. Solid, 15, 209–309 (1967).
A. E. Green and K. A. Lindsay, Thermoelasticity, J. Elast., 2, 1–7 (1972).
J. Ignaczak and M. Ostoja-Starzewski, Thermoelasticity with Finite Wave Speeds, Oxford University Press, Oxford (2009).
R. S. Dhaliwal and H. H. Sherief, Generalized thermoelasticity for anisotropic media, Quart. Appl. Math., 33, 1–8 (1980).
M. Schoenberg and D. Censor, Elastic waves in rotating media, Quart. Appl. Math., 31, 115–125 (1973).
D. S. Chandrasekharaiah and K. R. Srikantiah, Thermoelastic plane waves in a rotating solid, Acta Mech., 50, 211–219 (1984).
D. S. Chandrasekharaiah and K. R. Srikantiah, Thermoelastic plane waves without energy dissipation in a rotating body, Mech. Res. Commun., 24, 551–560 (1984).
F. Ahmad and A. Khan, Thermoelastic plane waves in rotating isotropic medium, Acta Mech., 136, 243–247 (1999).
C. M. Keith and S. Crampin, Seismic body waves in anisotropic media: Reflection and refraction at a plane interface, Geophys. J. Roy. Astron. Soc., 49, 181–208 (1977).
A. Chattopadhyay and S. Choudary, The reflection phenomena of P-waves in a medium of monoclinic type, Int. J. Eng. Sci., 33, 199–207 (1995).
A. Chattopadhyay, S. Saha, and M. Chakraboty, The reflection of SV-waves in a monoclinic medium, Indian J. Pure Appl. Math., 27, 1029–1042 (1996).
S. J. Singh, Comments on the reflection phenomena of SV-waves in a medium of monoclinic type, Int. J. Eng. Sci., 37, 407–410 (1986).
S. Singh and S. Khurana, Reflection of P and SV waves at the free surface of a monoclinic elastic half-space, Proc. Indian Acad. Sci., 80, 401–412 (1986).
B. Singh, Wave propagation in an anisotropic generalized thermoelastic solid, Indian J. Pure Appl. Math., 34, 1479–1485 (2003).
B. Singh, Dispersion relations in a generalized monoclinic thermoelastic solid half-space, J. Tech. Phys., 47, 119–129 (2006).
B. Singh, Reflection of plane waves at the free surface of a monoclinic thermoelastic solid half-space, Eur. J. Mech. Solids, 29, 911–916 (2010).
R. Kumar and M. Singh, Effects of rotating and imperfection on reflection and transmission of plane waves in anisotropic generalized thermoelastic media, J. Sound Vibr., 324, 773–797 (2009).
S. S. Singh and S. K. Tomar, Quasi-P waves at a corrugated interface between two dissimilar monoclinic elastic halfspaces, Int. J. Solids Struct., 44, 197–228 (2007).
B. Singh and A. K. Yadav, Plane waves in a transversely isotropic rotating magneto-thermo-elastic medium, J. Eng. Phys. Thermophys., 85, 1226–1232 (2012).
B. Singh and A. K. Yadav, Reflection of plane waves in a rotating transversely isotropic magneto-thermoelastic solid half-space, J. Theor. Appl. Mech. (Sofia), 42, 33–60 (2012).
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Published in Inzhenerno-Fizicheskii Zhurnal, Vol. 89, No. 2, pp. 417–427, March–April, 2016.
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Singh, B., Yadav, A.K. Plane Waves in a Rotating Monoclinic Magnetothermoelastic Medium. J Eng Phys Thermophy 89, 428–440 (2016). https://doi.org/10.1007/s10891-016-1393-9
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DOI: https://doi.org/10.1007/s10891-016-1393-9