Wave propagation in a piezoelectric plate with surface effect

Analysis of Piezoelectric Structures and Devices

Volumn , Issue , 2013, Pages 285-312

  Chen, Wei Qiu ^a  

^a ZHEJIANG UNIVERSITY   (China)

Author keywords

Dispersion; Effective boundary conditions; Piezoelectric plate; State space formulations; Surface effect; Wave propagation

Indexed keywords

BOUNDARY CONDITIONS; CONTINUUM MECHANICS; CRYSTALLOGRAPHY; DISPERSIONS; MATERIALS HANDLING EQUIPMENT; MOLECULAR DYNAMICS; MULTIVARIABLE CONTROL SYSTEMS; PIEZOELECTRIC DEVICES; PIEZOELECTRICITY; STATE SPACE METHODS; VECTOR SPACES; WAVE PROPAGATION;

DISPERSION RELATIONS; MOLECULAR DYNAMICS SIMULATIONS; PIEZOELECTRIC PLATE; STATE SPACE FORMULATION; SURFACE EFFECT; SURFACE PIEZOELECTRICITIES; THEORETICAL FRAMEWORK; WAVE PROPAGATION CHARACTERISTICS;

DISPERSION (WAVES);

EID: 84979172137     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1515/9783110297997.285     Document Type: Chapter

References (38)

1. Cammarata R C. Surface and interface stress effects in thin films. Prog. Surf. Sci., 1994, 46(1), 1-38.
2. Miller R E, Shenoy V B. Size-dependent elastic properties of nanosized structural elements. Nanotech., 2000, 11(3), 139-147.
3. Gurtin M E, Murdoch A I. A continuum theory of elastic material surfaces. Arch. Rat. Mech. Anal., 1975,57(4), 291-323.
4. Gurtin M E, Murdoch A I. Surface stress in solids. Int. J. Solids Struct., 1978, 14(6), 431-440.
5. Murdoch A I. The propagation of surface waves in bodies with material boundaries. J. Mech. Phys. Solids, 1976, 24(2-3), 137-146.
6. Gurtin M E, Murdoch A I. Effect of surface stress on wave propagation in solids. J. Appl. Phys., 1976, 47(10), 4414-4421.
7. Murdoch A I. The effect of interfacial stress on the propagation of Stoneley waves. J. Sound Vib., 1977, 50(1), 1-11.
8. Mindlin R D. High frequency vibrations of plated, crystal plates. In: Progress in Applied Mechanics. New York: MacMillan, 1963, 73-84.
9. Tiersten H F. Elastic surface waves guided by thin films. J. Appl. Phys., 1969, 40(2), 770-789.
10. Rokhlin S I, Wang Y J. Analysis of boundary conditions for elastic wave interaction with an interface between two solids. J. Acoust. Soc. Am., 1991, 89(2), 503-513.
11. Bovik P. On the modelling of thin interface layers in elastic and acoustic scattering problems. Quart. J. Mech. Appl. Math., 1994, 47(1), 17-42.
12. Niklasson A J, Datta S K, Dunn M L. On approximating guided waves in plates with thin anisotropic coatings by means of effective boundary conditions. J. Acoust. Soc. Am., 2000, 108(3), 924-933.
13. Niklasson A J, Datta S K, Dunn M L. On ultrasonic guided waves in a thin anisotropic layer lying between two isotropic layers. J. Acoust. Soc. Am., 2000, 108(5), 2005-2011.
14. Ting T C T. Steady waves in an anisotropic elastic layer attached to a half-space or between two half-spaces - a generalization of Love waves and Stoneley waves. Math. Mech. Solids, 2009, 14(1-2), 52-71.
15. Johansson G, Niklasson A J. Approximate dynamic boundary conditions for a thin piezoelectric layer. Int. J. Solids Struct., 2003, 40(13-14), 3477-3492.
16. Mauritssona K, Bostrom A, Folkow P D. Modelling of thin piezoelectric layers on plates. Wave Motion, 2008, 45(5), 616-628.
17. Thomson W T. Matrix solution for the vibration of non-uniform beams. J. Appl. Mech., 1950, 17(3), 337-339.
18. Thomson W T. Transmission of elastic waves through a stratified solid medium. J. Appl. Phys., 1950, 21(2), 89-93.
19. Kennett BLN. Seismic Wave Propagation in Stratified Media. Cambridge: Cambridge University Press, 1983.
20. Das Y C, Setlur A V. Method of initial functions in two-dimensional elastodynamic problems. J. Appl. Mech., 1970, 37(1), 137-140.
21. Bufler H. Theory of elasticity of a multilayered medium. J. Elast., 1971, 1(2), 125-143.
22. Bahar L Y. Transfer matrix approach to layered systems. J. Eng. Mech. Div., 1972, 98(5), 1159-1172.
23. Kameswara Rao N S V, Das Y C. A mixed method in elasticity. J. Appl. Mech., 1977, 44(1), 51-56.
24. Fan J R, Ye J Q. A series solution of the exact equation for thick orthotropic plates. Int. J. Solids Struct., 1990, 26(7), 773-778.
25. Ding H J, Chen W Q, Zhang L C. Elasticity of Transversely Isotropic Materials. Dordrecht: Springer, 2006.
26. Chen W Q, Ding H J. A state-space based stress analysis of multilayered spherical shell with spherical isotropy. J. Appl. Mech., 2001, 68(1), 109-114.
27. Chen W Q, Ding H J. Free vibration of multi-layered spherically isotropic hollow spheres. Int. J. Mech. Sci., 2001, 43(3), 667-680.
28. Chen W Q. Free vibration analysis of laminated piezoceramic hollow spheres. J. Acoust. Soc. Am., 2001, 109(1), 41-50.
29. Chen W Q, Ding H J, Xu R Q. Three-dimensional static analysis of multi-layered piezoelectric hollow spheres via the state space method. Int. J. Solids Struct., 2001, 38(28-29), 4921-4936.
30. Lur’e A I. Three-Dimensional Problems of the Theory of Elasticity. New York: Interscience Publishers, 1964.
31. Ding H J, Chen W Q. Three Dimensional Problems of Piezoelasticity. New York: Nova Science Publishers, 2001.
32. Tarn J Q. A refined state space formalism for piezothermoelasticity. Int. J. Solids Struct., 2008, 45(10), 3021-3032.
33. Ding H J, Chen W Q, Xu R Q. New state space formulations for transversely isotropic piezoelasticity with application. Mech. Res. Commun., 2000, 27(3), 319-326.
34. Chen W Q, Lee K Y. Alternative state space formulations for magnetoelectric thermoelasticity with transverse isotropy and the application to bending analysis of nonhomogeneous plates. Int. J. Solids Struct., 2003, 40(21), 5689-5705.
35. Pao Y H, Kaul R K. Waves and vibrations in isotropic and anisotropic plates. In: R. D. Mindlin and Applied Mechanics, edited by Herrmann G. New York: Pergamon, 1974, 149-195.
36. Dunn M L, Taya M. Electroelastic field concentrations in and around inhomogeneities in piezoelectric solids. J. Appl. Mech., 1994, 61(2), 474-475.
37. Achenbach J D. Wave Propagation in Elastic Solids. Amsterdam: North-Holland, 1973.
38. Bovik P. A comparison between the Tiersten model and O(H) boundary conditions for elastic surface waves guided by thin layers. J. Appl. Mech., 1996, 63(1), 162-167.