Effect of Micropolarity on the Propagation of Shear Waves in a Piezoelectric Layered Structure

Document Type: Research Paper

Authors

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

2 Department of Mathematics, Lovely Professional University, Phagwara(Research Scholar Punjab Technical University, Jalandhar), India

3 Department of Mathematics, Guru Nanak Dev Engineering College, Ludhiana, India

Abstract

This paper studies the propagation of shear waves in a composite structure consisting of a piezoelectric layer perfectly bonded over a micropolar elastic half space. The general dispersion equations for the existence of shear waves are obtained analytically in the closed form. Some particular cases have been discussed and in one special case the relation obtained is in agreement with existing results of the classical –Love wave equation. The micropolar and piezoelectric effects on the phase velocity are obtained for electrically open and mechanically free structure. To illustrate the utility of the problem numerical computations are carried out by considering PZT-4 as a piezoelectric and aluminium epoxy as micropolar elastic material. It is observed that the micropolarity present in the half space influence the phase velocity significantly in a particular region.  The micropolar effects on the phase velocity in the piezoelectric coupled structure can be used to design high performance acoustic wave devices.

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[1] Bleustein J.L., 1968, A new surface wave in piezoelectric materials, Applied Physics Letter 13(12): 412-413.
[2] Mindlin R.D., 1952, Forced thickness-shear and flexural vibrations of piezoelectric, Journal of Applied Physics 23: 83-88.
[3] Tiersten H. F., 1963, Thickness vibrations of piezoelectric plates, The Journal of the Acoustical Society of America 35: 53-58.
[4] Curtis R.G., Redwood M., 1973, Transverse surface waves on a piezoelectric material carrying a metal layer of finite thickness, Journal of Applied Physics 44: 2002-2007.
[5] Wang Q., Quek S.T., Varadan V.K., 2001, Love waves in piezoelectric coupled solid media, Smart Materials and Structures 10: 380-388.
[6] Qian Z.-H., Jin F., Wang Z., Kishimoto K., 2004, Dispersion relations for SH-wave propagation in periodic piezoelectric composite, International Journal of Engineering Science 42(7): 673-689.
[7] Qian Z.-H., Jin F., Wang Z., Kishimoto K., 2004, Love waves propagation in a piezoelectric layered structure with initial stresses, Acta Mechanica 171(1-2): 41-57.
[8] Qian Z.-H., Jin F., Hirose S., 2011, Dispersion characteristics of transverse surface waves in piezoelectric coupled solid media with hard metal interlayer, Ultrasonics 51: 853-856.
[9] Liu J., Wang Z.K., 2005, The propagation behavior of Love waves in a functionally graded layered piezoelectric structure, Smart Materials and Structures 14(1): 137-146.
[10] Liu J., Cao X.S., Wang Z.K., 2008, Love waves in a smart functionally graded piezoelectric composite structure, Acta Mechanica 208(1-2): 63-80.
[11] Son M.S., Kang Y.J., 2011, The effect of initial stress on the propagation behavior of SH waves in piezoelectric coupled plates, Ultrasonics 51: 489-495.
[12] Saroj P.K., Sahu S.A., 2017, Reflection of plane wave at traction-free surface of a pre-stressed functionally graded piezoelectric material (FGPM) half-space, Journal of Solid Mechanics 9(2): 411-422.
[13] Arefi M., 2016, Surface effect and non-local elasticity in wave propagation of functionally graded piezoelectric nano-rod excited to applied voltage, Applied Mathematics and Mechanics 37: 289-302.
[14] Arefi M., 2016, Analysis of wave in a functionally graded magneto-electroelastic nano-rod using nonlocal elasticity model subjected to electric and magnetic potentials, Acta Mechanica 227(9): 2529-2542.
[15] Arefi M., Zenkour A.M., 2016, Free vibration, wave propagation and tension analyses of a sandwich micro/nano rod subjected to electric potential using strain gradient theory, Material Research Express 3(11):115704.
[16] Arefi M., Zenkour A.M., 2017, Nonlocal electro-thermo-mechanical analysis of a sandwich nanoplate containing a Kelvin–Voigt viscoelastic nanoplate and two piezoelectric layers, Acta Mechanica 228(2): 475-494.
[17] Arefi M., Zenkour A.M., 2017, Size-dependent free vibration and dynamic analyses of piezo-electromagnetic sandwich nanoplates resting on viscoelastic foundation, Physica B 521: 188-197.
[18] Arefi M., Zenkour A.M., 2017, Vibration and bending analysis of a sandwich microbeam with two integrated piezo-magnetic face-sheets, Composite Structures 159: 479-490.
[19] Arefi M., Zenkour A.M., 2017, Influence of micro-length-scale parameters and inhomogeneities on the bending, free vibration and wave propagation analyses of a FG Timoshenko’s sandwich piezoelectric microbeam, Journal of Sandwich Structures & Materials (in press).
[20] Arefi M., Zenkour A.M., 2017 ,Wave propagation analysis of a functionally graded magneto-electro-elastic nanobeam rest on Visco-Pasternak foundation, Mechanics Research Communications 79: 51-62.
[21] Voigt W., 1887, Theoretische Studien über die Elastizitätsverhältnisse der Krystalle, Abhandlungen der Königlichen Gesellschaft der Wissenschaften in Göttingen, German.
[22] Eringen A.C., Suhubi E.S., 1964, Nonlinear theory of simple micro-elastic solid-I, International Journal of Engineering Science 2: 189-203.
[23] Eringen A.C., 1966, Linear theory of Micropolar elasticity, Journal of Mathematics and Mechanics 15: 909-923.
[24] Eringen A.C., 1999, Microcontinuum Field Theories-I, New York, Springer-Verlag.
[25] Singh B., Kumar R., 1998, Reflection and refraction of plane waves at an interface between micropolar elastic solid and viscoelastic solid, International Journal of Engineering Science 36(2): 119-135.
[26] Tomer S., 2005, Wave propagation in a micropolar elastic plate with voids, Journal of Vibration and Control 11: 849-863.
[27] Kumar R., Deswal S., 2006, Some problems of wave propagation in a micropolar elastic medium with voids, Journal of Vibration and Control 12(8): 849-879.
[28] Midya G.K., 2004, On Love-type surface waves in homogeneous micropolar elastic media, International Journal of Engineering Science 42(11-12): 1275-1288.
[29] Kumar R., Kaur M., Rajvanshi S.C., 2014, Propagation of waves in micropolar generalized thermoelastic materials with two temperatures bordered with layers or half-spaces of inviscid liquid, Latin American Journal of Solids and Structures 2(7): 1091-1113.
[30] KaurT., Sharma S.K., Singh A.K., 2017, Shear wave propagation in vertically heterogeneous viscoelastic layer over a micropolar elastic half-space, Mechanics of Advanced Materials and Structures 24(2): 149-156.
[31] Singh A.K., Kumar S., Dharmender, Mahto S., 2017, Influence of rectangular and parabolic irregularities on the propagation behavior of transverse wave in a piezoelectric layer: A comparative approach, Multidiscipline Modeling in Materials and Structures 13(2): 188-216.
[32] Kumar R., Kaur M., 2017, Reflection and transmission of plane waves at micropolar piezothermoelastic solids, Journal of Solid Mechanics 9(3): 508-526.
[33] Kundu S., Kumari A., Pandit D.K., Gupta S., 2017, Love wave propagation in heterogeneous micropolar media, Mechanics Research Communications 83: 6-11.
[34] Love A.E.H., 1920, Mathematical Theory of Elasticity, Cambridge University Press, Cambridge.
[35] Gauthier R.D., 1982, Experimental Investigation on Micropolar Media, Mechanics of Micropolar Media, World Scientific, Singapore.
[36] Liu J., Wang Y., Wang B., 2010, Propagation of shear horizontal surface waves in a layered piezoelectric half-space with an imperfect interface, IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control 57(8): 1875-1879.