Mathematical Study for the Rayleigh Wave Propagation in a Composite Structure with Piezoelectric Material

الموضوعات :

B Paswan ¹ (Department of Mathematics,Guru Ghasidas Vishwavidyalaya Bilaspur, Chhattisgarh-495009, India)
P Singh ² (Department of Mathematics and Computing, Indian Institute of Technology (Indian School of Mines) Dhanbad-826004, India---- Department of Mathematics,Buddha Post Graduate College, Kushinagar (Affiliated-DDU Gorakhpur University, Gorakhpur), Uttar Pradesh-274403, India)
Sanjeev A Sahu ³ (Department of Mathematics and Computing, Indian Institute of Technology (Indian School of Mines) Dhanbad-826004, India)

تاريخ الإرسال : 21 الأحد , رجب, 1444 تاريخ التأكيد : 12 الإثنين , رمضان, 1444 تاريخ الإصدار : 12 الخميس , ذو القعدة, 1444

الکلمات المفتاحية: Frequency equation, Corrugation, Generalized Rayleigh-type wave, Piezoelectricity, Initial stress,

ملخص المقالة :

The undulated characteristics of the irregular boundaries in the layered structure with piezoelectric materials generate some prominent effects on wave propagation. On the other hand, initial stress in the layered structure also play an important role in velocity characterization of the surface seismic waves. In light of the above, this paper studies the Rayleigh-type wave propagation in a composite structure with piezoelectric materials. Mathematical expressions for the mechanical displacement and electric potential function are obtained for both the piezoelectric layer and elastic substrate with the aid of coupled electromechanical field equations. Frequency equations for the waves are derived for both electrically open and short cases. The effects of the corrugation parameters, initial stress, piezoelectric constant, dielectric constant and thickness of the piezoelectric layer on the phase velocity of Rayleigh-type wave are discussed graphically for both the electrically open and short cases. Numerical examples and discussions are made to exhibit the findings graphically. The validation of the problem is made with the classical result.

المصادر:

1. Mindlin R.D., 1952, Forced thickness-shear and flexural vibrations of piezoelectric crystal plates, Journal of Applied Physics 23: 83-88.


2. Tiersten H.F., 1963, Wave propagation in an infinite piezoelectric plate, Journalof the Acoustical Society of America  35: 234-239.


3. Cheng N.C., Sun C.T., 1975, Wave propagation in two-layered piezoelectric plates, Journalof the Acoustical Society of America 57:


4. Romos R.R., Otero J.A., 1997, Wave propagation in a piezoelectric layer, Journal of Applied Physics 81: 7242-7247.


5. Mesquida A.A., Otero J.A., Ramos R.R., Comas F., 1998, Wave propagation in layered piezoelectric structures, Journal of Applied Physics 83: 4652-4659.


6. Liu G.R., Tani J., Ohyoshi T., 1991, Lamb waves in a functionally gradient material plates and its transient response part 1: theory; part 2: calculation result, Trans, The Japan Society of Mechanical Engineers 57A: 131-142.


7. Liu H., Wang T.J., Wang Z. K., Kuang Z.B., 2002, Effect of a biasing electric field on the propagation of symmetric Lamb waves in piezoelectric plates, International Journal of Solids and Structures39: 2031-2049.


8. Liu H., Wang T.J., Wang Z.K., Kuang Z.B., 2002, Effect of a biasing electric field on the propagation of anti-symmetric Lamb waves in piezoelectric plates, International Journal of Solids and Structures 39(7): 1777-1790.


9. Liu J., Wang Z., 2004, Study on the propagation of Rayleigh surface waves in a graded half-space, Chinese Journal of Applied Mechanics 21: 106-109.


10. Qian Z., Jin F., Kishimoto K., Wang Z., 2004, Effect of initial stress on the propagation behavior of SH-waves in multilayered piezoelectric composite structures, Sensors and Actuators A 112: 368-375.


11. Du J., Jin X., Wang J., Xian K., 2007, Love wave propagation in functionally graded piezoelectric material layer, Ultrasonics 46(1): 13-22.


12. Cao X., Jin F., Jeon I., 2009, Rayleigh surface waves in a piezoelectric wafer with subsurface damage, Applied Physics Letters 95: 261906.


13. Singh P., Singh A.K., Paswan B., Chattopadhyay A., 2022, Mathematical study on reflection and transmission of plane waves in a rotating piezo-thermo-elastic composite structure, Mechanics of Advanced Materials and Structures 2022: 1-12.


14. Guha S., Singh A.K., 2021, Plane wave reflection/transmission in imperfectly bonded initially stressed rotating piezothermoelastic fiber-reinforced composite half-spaces, European Journal of Mechanics-A/Solids88: 104242.


15. Saha S., Singh A.K., Chattopadhyay A., 2020, Analysis of reflection and refraction of plane wave at the separating interface of two functionally graded incompressible monoclinic media under initial stress and gravity, The European Physical Journal Plus135(2):1-31.


16. 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.


17. Li P., Jin F., 2015, Excitation and propagation of shear horizontal waves in a piezoelectric layer imperfectly bonded to a metal or elastic substrate, Acta Mechanica 226: 267-284.


18. Saroj P.K., Sahu S.A., Chaudhary S., Chattopadhyay A., 2015, Love-type waves in functionally graded piezoelectric material (FGPM) sandwiched initially stressed layer and elastic substrate, Waves in Random and Complex Media 25(4): 608-627.


19. Hurd R.A., 1954, The propagation of an electromagnetic wave along an infinite corrugated surface, Canadian Journal of Physics 32(12): 727-734.


20. Glass N.E., Maradudin A.A., 1983, Leaky surface‐elastic waves on both flat and strongly corrugated surfaces for isotropic, Non Dissipative Media 54:


21. Singh S.S., 2011, Love wave at a layer medium bounded by irregular boundary surfaces, Journal of Vibrationand Control 17: 789-795.


22. Singh A.K., Lakshman A., Chattopadhyay A., 2015, Influence of corrugated boundary surface and reinforcement of fiber-reinforced layer on propagation of torsional surface wave, Journal of Vibration and Control 23(9): 1417-1436.


23. Abd-Alla A.M., Hammad H.S., Abo-Dahab S.M., 2004, Rayleigh waves in a magnetoelastic half-space of orthotropic material under influence of initial stress and gravity field, Applied Mathematics and Computation 154(2): 583-597.


24. Abd-Alla A.M., Abo-Dahab S.M., 2004, Rayleigh waves in magneto-thermo-viscoelastic solid with thermal relaxation times, Applied Mathematicsand Computation 149: 861-877.


25. Abo-Dahab S.M., 2015, Propagation of stoneley waves in magneto-thermoelastic materials with voids and two relaxation times, Journal of Vibration and Control 21(6): 1144-1153.


26. Rayleigh J.W.S., 1887, On waves propagating along the plane surface of an elastic solid, Proceedingsof the London Mathematical Society 17: 4-11.


27. Weis R.S., Gaylord T.K., 1985, Lithium niobate: summary of physical properties and crystal structure, Journal of Applied Physics A 37: 191-203.