Reflection and Transmission of Plane Waves at Micropolar Piezothermoelastic Solids

Document Type: Research Paper

Authors

1 Department of Mathematics, Kurukshetra University, Kurukshetra 136119, India

2 Department of Mathematics, Sri Guru Teg Bahadur Khalsa College, Anandpur Sahib, Punjab 140118, India

Abstract

The present investigation analysis a problem of r­­­eflection and transmission at an interface of two micropolar orthotropic piezothermoelastic media. The basic equations and constitutive relations for micropolar orthotropic piezothermoelastic media for G-L theory are derived. The expressions for amplitude ratios corresponding to reflected and transmitted waves are derived analytically. The effect of angle of incidence, frequency, micropolarity, thermopiezoelectric interactions on the reflected and transmitted waves are studied numerically for a specific model. Some special cases of interest one are also deduced. 

Keywords


[1] Eringen A.C.,1996, Linear theory of micropolar elasticity, Journal of Mathematics and Mechanics 15: 909-923.
[2] Eringen A.C., 1970, Foundations of Micropolar Thermoelasticity, Course Held at the Department for Mechanics of Deformable Bodies, Springer.
[3] Eringen A.C., 1992, Microcontinuum Field Theory I, Foundations and Solids, Springer, New York.
[4] Eringen A.C., Suhubi E.S., 1964, Non-linear theory of aimple micro-elastic solids, International Journal of Engineering Science 2:189-203.
[5] Green A.E., Lindsay K.A., 1972, Thermoelasticity, Journal of Elasticity 2: 1-7.
[6] Abd-Alla A.N., Hamdan A.M., Giorgio I., Del Vescovo D., 2014, The mathematical model of reflection and refraction of longitudinal waves in thermo-piezoelectric materials, Archive of Applied Mechanics 84(9): 1229-1248.
[7] Abd-Alla A.N., Giorgio I., Galantucci L., Hamdan A.M., Del Vescovo D., 2016, Wave reflection at a free interface in an anisotropic pyroelectric medium with nonclassical thermoelasticity, Continuum Mechanics and Thermodynamics 28(1-2): 67-84.
[8] Abd-Alla A.N., Alshaikh F.A., 2009, Reflection and refraction of plane quasi-longitudinal waves at an interface of two piezoelectric media under initial stresses, Archive of Applied Mechanics 79(9): 843-857.
[9] Abd-Alla A.N., Alshaikh F.A., 2009, The effect of the initial stresses on the reflection and transmission of plane quasi-vertical transverse waves in piezoelectric materials, Proceedings of World Academy of Science, Engineering and Technology 38: 660-668.
[10] Abd-Alla A.N., Alshaikh F.A., Al-Hossain A.Y., 2012, The reflection phenomena of quasi-vertical transverse waves in piezoelectric medium under initial stresses, Meccanica 47(3): 731-744.
[11] Iesan D., 1973, The plane micropolar strain of orthotropic elastic solids, Archiwum Mechaniki Stosowanej 25: 547-561.
[12] Iesan D., 1974, Torsion of anisotropic micropolar elastic cylinders, Zeitschrift für Angewandte Mathematik und Mechanik 54: 773-779.
[13] Iesan D., 1974, Bending of orthotropic micropolar elastic beams by terminal couples, Analele Stiintifice Ale Universitatii Iasi 20: 411-418.
[14] Chandrasekharaiah D.S., 1984, A temperature-rate-dependent theory of thermopiezoelectricity, Journal of Thermal Stresses 7: 293-306.
[15] Chandrasekharaiah D.S.,1988, A generalized linear thermoelasticity theory for piezoelectric media, Acta Mechanica 71: 39-49.
[16] Alshaikh F.A., 2012, The mathematical modelling for studying the influence of the initial stresses and relaxation times on reflection and refraction waves in piezothermoelastic half-space, Applied Mathematics 3(8): 819-832.
[17] Alshaikh F.A., 2012, Reflection of quasi vertical transverse waves in the thermo-piezoelectric material under initial stress (Green- Lindsay Model), International Journal of Pure and Applied Sciences and Technology 13: 27-39.
[18] Sharma J.N., Walia V., Gupta S.K., 2008, Reflection of piezo-thermoelastic waves from the charge and stress free boundary of a transversely isotropic half space, International Journal of Engineering Science 46(2):131-146.
[19] Othman M.I.A., 2015,The effect of rotation on piezothermoelastic medium using different theories, Structural Engineering and Mechanics 56(4): 649-665.
[20] Othman M.I.A., Atwa S.Y., Hasona W.M., Ahmed E.A.A., 2015, Propagation of plane waves in generalized piezo-thermoelastic medium: Comparison of different theories, International Journal of Innovative Research in Science, Engineering and Technology 4(4): 2292-2300.
[21] Hou P.F., Luo W., Leung Y.T., 2008, A point heat source on the surface of a semi-infinite transverse isotropic piezothermoelastic material, SME Journal of Applied Mechanics 75:1-8.
[22] Mindlin R.D., 1961, On the Equations of Motion of Piezoelectric Crystals, Problems of Continuum Mechanics, SIAM, Philadelphia.
[23] Kumar R., Choudhary S., 2002, Mechanical sources in orthotropic micropolar continua, Proceedings of the Indian Academy of Sciences (Earth and Planetary Sciences) 111: 133-141.
[24] Kumar R., Choudhary S., 2002, Influence of Green’s function for orthotropic micropolar continua, Archive of Mechanics 54: 185-198.
[25] Kumar R., Choudhary S., 2002, Dynamical behavior of orthotropic micropolar elastic medium, Journal of Vibration and Control 8: 1053-1069.
[26] Kumar R., Choudhary S., 2003, Response of orthotropic microploar elastic medium due to various sources, Meccanica 38: 349-368.
[27] Kumar R., Choudhary S., 2004, Response of orthotropic micropolar elastic medium due to time harmonic sources, Sadhana 29: 83-92.
[28] Nakamura S., Benedict R., Lakes R., 1984, Finite element method for orthotropic micropolar elasticity, International, Journal of Engineering Science 22: 319-330.
[29] Nowacki W., 1966, Couple stress in the theory of thermoelasticity, Irreversible Aspects of Continuum Mechanics and Transfer of Physical Characteristics in Moving Fluids, Springer,Verlag.
[30] Nowacki W.,1978, Some general theorems of thermo-piezoelectricity, Journal of Thermal Stresses 1: 171-182.
[31] Nowacki W., 1979, Foundations of Linear Piezoelectricity, Electromagnetic Interactions in Elastic Solids, Springer, Wein.
[32] Nowacki W., 1983, Mathematical Models of Phenomenological Piezo-Electricity, New Problems in Mechanics of Continua, University of Waterloo Press, Waterloo, Ontario.
[33] Slaughter W.S., 2002, The Linearized Theory of Elasticity, Birkhauser, Basel.
[34] Chen W.Q., 2000, On the general solution for piezothermoelastic for transverse isotropy with application, ASME, Journal of Applied Mechanics 67: 705-711.
[35] Guo X., Wei P., 2014, Effects of initial stress on the reflection and transmission waves at the interface between two piezoelectric half spaces, International Journal of Solids and Structures 51(21): 3735-3751.
[36] Pang Y., Wang Y. S., Liu J.X., Fang D. N., 2008, Reflection and refraction of plane waves at the interface between piezoelectric and piezomagnetic media, International Journal of Engineering Science 46: 1098-1110.
[37] Kuang Z.B., Yuan X.G.,2011, Reflection and transmission of waves in pyroelectric and piezoelectric materials , Journal of Sound and Vibration 330(6):1111-1120.