Smart Structures and Systems

  • 제22권3호
  • /
  • Pages.341-358
  • /
  • 2018
  • /
  • 1738-1584(pISSN)
  • /
  • 1738-1991(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Influence of loose bonding, initial stress and reinforcement on Love-type wave propagating in a functionally graded piezoelectric composite structure

  • Singh, Abhishek K. (Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines)) ;
  • Parween, Zeenat (Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines)) ;
  • Chaki, Mriganka S. (Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines)) ;
  • Mahto, Shruti (Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines))
  • 투고 : 2017.09.22
  • 심사 : 2018.04.09
  • 발행 : 2018.09.25
⟨ 이전 논문 다음 논문 ⟩

초록

This present study investigates Love-type wave propagation in composite structure consists of a loosely bonded functionally graded piezoelectric material (FGPM) stratum lying over a functionally graded initially-stressed fibre-reinforced material (FGIFM) substrate. The closed-form expressions of the dispersion relation have been obtained analytically for both the cases of electrically open and electrically short conditions. Some special cases of the problem have also been studied and the obtained results are found in well-agreement with the classical Love wave equation. The emphatic influence of wave number, bonding parameter associated with bonding of stratum with substrate of the composite structure, piezoelectric coefficient as well as dielectric constant of the piezoelectric stratum, horizontal initial stresses, and functional gradedness of the composite structure on the phase velocity of Love-type wave has been reported and illustrated through numerical computation along with graphical demonstration in both the cases of electrically open and electrically short condition for the reinforced and reinforced-free composite structure. Comparative study has been carried out to analyze the distinct cases associated with functional gradedness of the composite structure and also various cases which reveals the influence of piezoelectricity, reinforcement and horizontal initial stress acting in the composite structure, and bonding of the stratum and substrate of the composite structure in context of the present problem which serves as one of the major highlights of the study.

키워드

과제정보

연구 과제번호 : Mathematical Study on Wave Propagation Aspects in Piezoelectric Composite Structures with Complexities

연구 과제 주관 기관 : Department of Science and Technology, Science & Engineering Research Board (DSTSERB)

참고문헌

  1. Adkins, J.E. (1956), "Finite plane deformation of thin elastic sheets reinforced with inextensible cords", Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 249(961), 125-150. https://doi.org/10.1098/rsta.1956.0017
  2. Belfield, A.J., Rogers, T.G. and Spencer, A.J.M. (1983), "Stress in elastic plates reinforced by fibres lying in concentric circles", J. Mech. Phys. Solids, 31(1), 25-54. https://doi.org/10.1016/0022-5096(83)90018-2
  3. Biot, M.A. and Drucker, D.C. (1965), "Mechanics of incremental deformation", J. Appl. Mech., 32, 957.
  4. Chattopadhyay, A. and Kar, B.K. (1978), "On the dispersion curves of Love type waves in an initially stressed crustal layer having an irregular interface", Geophys. Res. Bull., 16(1), 13-23.
  5. Chattopadhyay, A. and Singh, A.K. (2012), "G-type seismic waves in fibre reinforced media", Meccanica, 47(7), 1775-1785. https://doi.org/10.1007/s11012-012-9553-2
  6. Chen, W.Q. and Lee, K.Y. (2004), "Exact solution of angle-ply piezoelectric laminates in cylindrical bending with interfacial imperfections", Compos. Struct., 65(3), 329-337. https://doi.org/10.1016/j.compstruct.2003.11.008
  7. Chttopadhyay, A. and De, R.K. (1981), "Propagation of Love type waves in a visco-elastic initially stressed layer overlying a visco-elastic half-space with irregular interface", Rev. Roum. Sci. Tech. Mec. Appl. Tome, 26(3), 449-460.
  8. Dey, S., Roy, N. and Dutta, A. (1989), "Propagation of Love waves in an initially stressed anisotropic porous layer lying over a pre-stressed non-homogeneous elastic half-space", Acta Geophysica Polonica, 37(1), 21-36.
  9. Du, J., Jin, X., Wang, J. and Xian, K. (2007), "Love wave propagation in functionally graded piezoelectric material layer", Ultrasonics, 46(1), 13-22. https://doi.org/10.1016/j.ultras.2006.09.004
  10. Ewing, M., Jardetzky, W.S. and Press, F. (1957), Elastic waves in layered media, Mc Graw-Hill, New York.
  11. Gillis, P.P. (1984), "Calculating the elastic constants of graphite. Carbon, 22(4), 387-391. https://doi.org/10.1016/0008-6223(84)90010-1
  12. Han, X. and Liu, G.R.(2003), "Elastic waves in a functionally graded piezoelectric cylinder", Smart Mater. Struct., 12(6), 962. https://doi.org/10.1088/0964-1726/12/6/014
  13. Hashin, Z. and Rosen, B.W. (1964), "The elastic moduli of fiberreinforced materials", J. Appl. Mech., 31(2), 223-232. https://doi.org/10.1115/1.3629590
  14. Ichinose, N., Miyamoto, N. and Takahashi, S. (2004), "Ultrasonic transducers with functionally graded piezoelectric ceramics", J. Eur. Ceramic Soc., 24(6), 1681-1685. https://doi.org/10.1016/S0955-2219(03)00599-5
  15. Kaur, T., Sharma, S.K. and Singh, A.K. (2016), "Influence of imperfectly bonded micropolar elastic half-space with nonhomogeneous viscoelastic layer on propagation behavior of shear wave", Waves in Random and Complex Media, 1-21.
  16. Khurana, P. and Vashisth, A.K. (2001), "Love wave propagation in a pre-stressed medium", Indian J. Pure Appl. Math., 32(8), 1201-1208.
  17. Lim, C.W. and Lau, C.W.H. (2005), "A new two-dimensional model for electro-mechanical response of thick laminated piezoelectric actuator", Int. J. Solids Struct., 42(20), 5589-5611. https://doi.org/10.1016/j.ijsolstr.2005.02.050
  18. Liu, H., Wang, Z. K. and Wang, T. J. (2001), "Effect of initial stress on the propagation behavior of Love waves in a layered piezoelectric structure", Int. J. Solids Struct., 38(1), 37-51. https://doi.org/10.1016/S0020-7683(00)00009-3
  19. Liu, G.R. and Tani, J. (1994), "Surface waves in functionally gradient piezoelectric plates", J. Vib. Acoust., 116(4), 440-448. https://doi.org/10.1115/1.2930447
  20. Liu, G.R., Dai, K.Y., Han, X. and Ohyoshi, T. (2003), "Dispersion of waves and characteristic wave surfaces in functionally graded piezoelectric plates", J. Sound Vib., 268(1), 131-147. https://doi.org/10.1016/S0022-460X(02)01494-3
  21. Liu, G.R. and Tani, J. (1991), "Characteristic of wave propagation in functionally gradient piezoelectric material plates and its response analysis. Part 1: theory; Part 2: calculation results", T. Japan Soc. Mech. Engineers, 57 (541), 2122-2133. https://doi.org/10.1299/kikaia.57.2122
  22. Love, A.E.H. (2013), A treatise on the mathematical theory of elasticity (Vol. 1), Cambridge University Press.
  23. Maugin, G.A. (1981), "Wave motion in magnetizable deformable solids", Int. J. Eng. Sci., 19(3), 321-388. https://doi.org/10.1016/0020-7225(81)90059-8
  24. Murty, G.S. (1975), "A theoretical model for the attenuation and dispersion of Stoneley waves at the loosely bonded interface of elastic half spaces", Phys. Earth Planetary Interiors, 11(1), 65-79. https://doi.org/10.1016/0031-9201(75)90076-X
  25. Murty, G.S. (1976), "Reflection, transmission and attenuation of elastic waves at a loosely-bonded interface of two half spaces", Geophys. J. Int., 44(2), 389-404. https://doi.org/10.1111/j.1365-246X.1976.tb03663.x
  26. Nagy, P.B. (1992), "Ultrasonic classification of imperfect interfaces", J. Nondestruct. Eval., 11(3-4), 127-139. https://doi.org/10.1007/BF00566404
  27. Ootao, Y. and Tanigawa, Y. (2000), "Three-dimensional transient piezothermoelasticity in functionally graded rectangular plate bonded to a piezoelectric plate", Int. J. Solids Struct., 37(32), 4377-4401. https://doi.org/10.1016/S0020-7683(99)00257-7
  28. Rabin, B.H. and Shiota, I. (1995), "Functionally gradient materials", MRS Bulletin, 20(1), 14-18.
  29. Schoenberg, M. (1980), "Elastic wave behavior across linear slip interfaces", J. Acoust. Soc. Am., 68(5), 1516-1521. https://doi.org/10.1121/1.385077
  30. Singh, A.K., Kumar, S. and Chattopadhyay, A. (2015), "Love-type wave propagation in a piezoelectric structure with irregularity", Int. J. Eng. Sci., 89, 35-60. https://doi.org/10.1016/j.ijengsci.2014.11.008
  31. Singh, A.K., Chaki, M.S., Hazra, B. and Mahto, S. (2017), "Influence of imperfectly bonded piezoelectric layer with irregularity on propagation of Love-type wave in a reinforced composite structure", Struct. Eng. Mech., 62(3), 325-344. https://doi.org/10.12989/sem.2017.62.3.325
  32. Singh, A.K., Parween, Z. and Kumar, S. (2016), "Love-type wave propagation in a corrugated piezoelectric structure", J. Intel. Mat. Syst. Str., 1045389X16635843.
  33. Spencer, A.J.M. (1972), Deformation of Fibre-reinforced material. Oxford University, United Kingdom.
  34. Termonia, Y. (1990), "Fibre coating as a means to compensate for poor adhesion in fibre-reinforced materials", J. Mater. Sci., 25(1), 103-106. https://doi.org/10.1007/BF00544192
  35. Tiersten, H.F. (1969), Linear Piezo-electric Plate Vibration. New York, Plenum Press.