Surface wave propagation in functionally graded piezoelectric material: An analytical solution

Abstract

Wentzel–Kramers–Brillouin approximation technique serves as a powerful tool to find the particle displacements due to surface wave propagation in bedded structure with distinct material properties. This study is carried out to investigate the transference of Love-type waves in functionally graded piezoelectric material layer bonded between viscous liquid and pre-stressed piezoelectric half-space. Following the elastic wave theory, the mathematical model is established. Wentzel–Kramers–Brillouin method is applied to obtain the theoretical derivations in functionally graded piezoelectric material stratum where variation in material gradients is taken exponentially. Separation of variables method is employed to obtain the displacement components in viscous liquid and piezoelectric medium. Dispersion equations for considered surface wave are obtained in both electrically open and short cases. Profound effect of material gradient coefficient on phase velocity has been remarkably established. Some numerical examples are carried out and represented through graphs. The considered model facilitates a theoretical foundation and practical application for the development of surface acoustic wave devices.

Keywords

Viscous liquid Wentzel–Kramers–Brillouin method functionally graded piezoelectric material initial stress dispersion relation

Get full access to this article

View all access options for this article.

References

Červený

Ravindra

(1971) Theory of Seismic Head Waves. Toronto, ON, Canada: University of Toronto Press.

Chaudhary

Sahu

Singhal

(2017) Analytic model for Rayleigh wave propagation in piezoelectric layer overlaid orthotropic substratum. Acta Mechanica 228(2): 495–529.

Jin

Wang

et al . (2007) Love wave propagation in functionally graded piezoelectric material layer. Ultrasonics 46: 13–22.

Xian

Yong

et al . (2010) SH-wave propagation in layered functionally graded piezoelectric medium structure loaded with viscous liquid. Acta Mechanica 212: 271–281.

Fröman

(2002) Physical Problems Solved by the Phase-Integral Method. Cambridge: Cambridge University Press.

Guo

Sun

(2008) Propagation of Bleustein–Gulyaev wave in 6 mm piezoelectric materials loaded with viscous liquid. International Journal of Solids and Structures 45(13): 3699–3710.

Han

Liu

(2003) Elastic waves in a functionally graded piezoelectric cylinder. Smart Materials and Structures 12: 962–971.

Han

Liu

Lam

(2001) Transient waves in plates of functionally graded materials. International Journal of Numerical Methods in Engineering 52: 851–865.

Hua

LIU

Yang

Liu

(2007) Love waves in layered graded composite structures with imperfectly bonded interface. Chinese Journal of Aeronautics 20(3): 210–214.

10.

Bernhard

Michael

(1997) Properties of Love waves: applications in sensors. Smart Materials and Structures 6: 668–679.

11.

Jin

Qian

Wang

et al . (2005) Propagation behavior of Love waves in a piezoelectric layered structure with inhomogeneous initial stress. Smart Materials and Structures 14: 515–523.

12.

Jones

(1992) The application of the WKB approximation to the calculation of the scattering of radio waves from overdense meteor trains. Planetary and Space Science 40(11): 1487–1497.

13.

Lee

Kuo

(2006) Leaky Lamb wave of a piezoelectric plate subjected to conductive fluid loading: theoretical analysis and numerical calculation. Journal of Applied Physics 100(7): 073519.

14.

Wang

Huang

(2004) Love waves in functionally graded piezoelectric materials. International Journal of Solids and Structures 41: 7309–7328.

15.

Liu

Tani

(1992) SH surface waves in functionally gradient piezoelectric material plates. Transactions of the Japan Society of Mechanical Engineers 58: 504–507.

16.

Liu

Wang

(2001) Effect of initial stresses on the propagation behavior of Love waves in a layered piezoelectric structure. International Journal of Solids and Structures 38: 37–51.

17.

Morsbøl

Sorokin

Peake

(2016) A WKB approximation of elastic waves travelling on a shell of revolution. Journal of Sound and Vibration 375: 162–186.

18.

Qian

Jin

Wang

et al . (2004) Love waves propagation in a piezoelectric layered structure with initial stresses. Acta Mechanica 171: 41–57.

19.

Qian

Jin

Wang

et al . (2007) Transverse surface waves on a piezoelectric material carrying a functionally graded layer of finite thickness. International Journal of Engineering Science 45: 455–466.

20.

Shulga

Zinchuk

(2005) Dispersion of surface waves in a periodically laminated piezoelectric half-space with liquid upper layer. International Applied Mechanics 41(3): 272–276.

21.

Wang

Huang

(1995) Stress intensification near an elliptic crack border. Theoretical and Applied Fracture Mechanics 22(3): 229–237.

22.

(2000) Surface waves in coated anisotropic medium loaded with viscous liquid. Journal of Applied Mechanics: Transactions of the ASME 67: 262–266.