Response of Two-Temperature on the Energy Ratios at Elastic-Piezothermoelastic Interface
Subject Areas : Mechanics of Solids
1 - Department of Mathematics, Kurukshetra University, Kurukshetra 136119, Haryana, India
2 - Department of Mathematics, Kurukshetra University, Kurukshetra 136119, Haryana, India
Keywords: Piezothermoelastic, Orthotropic, Energy ratios, Reflection, Transmission, Amplitude ratios,
Abstract :
In the present investigation the reflection and transmission phenomenon of plane waves between two half spaces elastic and orthotropic piezothermoelastic with two-temperature theory is discussed. A piezothermoelastic solid half space is assumed to be loaded with an elastic half space. Due to the phenomenon, four qausi waves are obtained; quasi longitudinal (qP) wave, quasi transverse (qS) wave, quasi thermal (qT) wave and electric potential wave (eP). It is found that the amplitude ratios of various reflected and refracted waves are functions of angle of incidence, frequency of incident wave and are influenced by the piezothermoelastic properties of media. The energy ratios are computed numerically using amplitude ratios for a particular model of graphite and cadmium selenide (CdSe). The variations of energy ratios with angle of incidence are shown graphically depicting the effect of two-temperature. The conservation of energy across the interface is justified. A particular case of interest is also deduced from the present investigation.
[1] Chen P. J., Gurtin M. E., 1968, On a theory of heat conduction involving two temperatures, The Zeitschrift für Angewandte Mathematik und Physik 19: 614-627.
[2] Chen P. J., Gurtin M. E., Williams W. O., 1968, A note on non-simple heat conduction, The Zeitschrift für Angewandte Mathematik und Physik 19: 969-970.
[3] Chen P. J., Gurtin M. E., Williams W. O., 1969, On the thermodynamics of non-simple elastic materials with two temperatures, The Zeitschrift für Angewandte Mathematik und Physik 20(1): 107-112.
[4] Sharma K., Marin M., 2013, Effect of distinct conductive and thermodynamic temperatures on the reflection of plane waves in micropolar elastic half-space, Applied Mathematics Physics 75(2): 121-32.
[5] Kumar R., Vashishth A. K., Ghangas S., 2018, Waves in anisotropic thermoelastic medium with phase lag, two-temperature and void, Materials Physics and Mechanics 35: 126-138.
[6] Mindlin R.D., 1974, Equation of high frequency of thermopiezoelectric crystals plates, International Journal of Solids and Structures 10: 625-637.
[7] Nowacki W., 1978, Some general theorems of thermo-piezoelectricity, Journal of Thermal Stresses 1: 171-182.
[8] Nowacki W., 1979, Foundation of Linear Piezoelectricity, Interactions in Elastic Solids, Springer, Wein.
[9] Vashishth A.K., Sukhija H., 2014, Inhomogeneous waves at the boundary of an anisotropic piezo-thermoelastic medium, Acta Mechanica 225: 3325-3338.
[10] Vashishth A.K., Sukhija H., 2015, Reflection and transmission of plane waves from fluid piezothermoelastic solid interface, Applied Mathematics and Mechanics 36(1): 11-36.
[11] Vashishth A.K., Sukhija H., 2017, Inhomogeneous waves in porous piezo-thermoelastic solids, Acta Mechanica 228: 1891-1907.
[12] Kumar R., Sharma P., 2017, Effect of fractional order on energy ratios at the boundary surface of elastic-piezothermoelastic media, Coupled Systems Mechanics 6(2):157-174.
[13] Marin M., Ochsner A., 2017, An initial boundary value problem for modelling a piezoelectric dipolar body, Continuum Mechanics and Thermodynamics 32(2): 267-78.
[14] Sharma M.D., 2018, Reflection–refraction of attenuated waves at the interface between a thermo-poroelastic medium and a thermoelastic medium, Waves in Random and Complex Media 28(3): 570-587.
[15] Kumar R., Sharma P., 2020, Basic theorems and wave propagation in a piezothermoelastic medium with dual phase lag, Indian Journal of Physics 94: 1975-1992.
[16] Bassiouny E., Youssef H. M., 2008, Two-temperature generalised thermopiezoelasticity of finite rod subjected to different types of thermal loadings, Journal of Thermal Stresses 31(1): 233-245.
[17] Ezzat M.A., El-Karamany A.S., Awad E. S., 2010, On the coupled theory of thermo-piezoelectric/ piezomagnetic materials with two-temperature, Canadian Journal of Physics 88(5): 307-315.
[18] Tzou H. S., Bao Y., 1995, A theory on anisotropic piezothermoelastic shell laminates with sensor/actuator applications, Journal of Sound and Vibration 184(3): 453-473.
[19] Bullen, K. E., 1963, An Introduction to the Theory of Seismology, Cambridge University Press, England.