The study of dynamic behavior of functionally graded piezoelectric materials and an application to a contact problem
Authors:
B. M. Singh, J. Rokne and R. S. Dhaliwal
Journal:
Quart. Appl. Math. 65 (2007), 155-162
MSC (2000):
Primary 74A30
DOI:
https://doi.org/10.1090/S0033-569X-07-01029-0
Published electronically:
February 12, 2007
MathSciNet review:
2313154
Full-text PDF Free Access
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Abstract: In the present paper, the dynamic behavior of functionally graded piezoelectric materials is investigated when it is under anti-plane mechanical loading and in-plane electrical loading. It is assumed that the shear modulus, the piezoelectric modulus, the dielectric modulus and mass density of FGPM vary continuously as functions of $X$ and $Y$. By using Fourier transforms the solution of equilibrium equations is obtained in closed form. The expressions for displacement and electrical potential are obtained in terms of one unknown function. Finally the results are applied to obtain a solution of the moving contact problem on the surface of the functionally graded piezoelectric material (FGPM).
References
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References
- Zhu, X., Wang, Q. and Meng, Z., A functionally graded piezoelectric actuator prepared by metallurgical process in PMN-PZ-PT system. J. Mater. Sci. Lett. 14 (1995), pp. 516-518.
- Zhu, Z., Zhu, J., Zhou, S., Li, Q. and Liu, Z., Microstructures of the monomorph piezoelectric ceramic actuators with functionally gradient sensor. Actuators A74 (1999), pp. 198-202.
- Wang B. L., A mode III crack in functionally graded piezoelectric materials. Mech. Res. Commun. 30 (2003), pp. 151-159.
- Wang B. L. and Zhang, X. H., A mode III crack in a functionally graded piezoelectric material strip. ASME J. Appl. Mech. 71 (2004) pp. 327-333.
- Li, Chunya and Weng, G. J., Antiplane Crack Problem in Functionally Graded Piezoelectric Materials. ASME, J. Appl. Mech. 69 (2002) pp. 481-488.
- Wu, C. M., Kahn, M. and Moy W., Piezoelectric ceramics with functional gradients, a new application in material design. J. Am. Ceramic Soc. 79 (1996) pp. 809-812.
- Lee, P. C. Y. and Yu, J. D., Governing equations for a piezoelectric plate with graded properties across the thickness. IEEE Trans. Ultrason. Ferroelectr. Freq Control 45 (1998) pp. 236-250.
- Hu, K. Q., Zhong, Z. and Jin, B., Anti-plane shear crack in a functionally gradient piezoelectric material. Acta Mech. Solida Sin. 15 (2002), pp. 140-148.
- Hu, K. Q., Zhong, Z. and Jin, B., Electroelastic intensification near anti-plane crack in a functionally gradient piezoelectric strip. Acta Mech. Solida Sin. 16 (2003), pp. 197-204.
- Hu, K. Q., Zhong, Z. and Jin, B., Anti-plane shear crack in a functionally gradient piezoelectric layer bonded to dissimilar half-spaces. Int. J. Mech. Sci. 47 (2005), pp. 82-93.
- Jin, B. and Zhong, Z., A moving mode-III crack in functionally graded piezoelectric material: permeable problem. Mech. Research Commun.29, (2002), pp. 217-224.
- Li, C., and Weng, G.J., Yoffe-type moving crack in a functionally graded piezoelectric material. Proc. R. Soc. Lond. A. 458, (2002), pp. 381-399. MR 1889934 (2002m:74046)
- Kwon, J. H., Lee, K. Y. and Kwon, S. M., Moving crack in a piezoelectric ceramic strip under anti-plane loading. Mech. Res. Commu. 27 (2000), pp. 327-332.
- Kwon, S. M. and Lee, K. Y., Constant moving crack in a piezoelectric block: anti-plane problem, Mech. Mater. 33 (2001), pp. 649-657.
- Kwon, S. M., Choi, H. S. and Lee, K. Y., Moving eccentric crack in a piezoelectric strip bonded to two elastic materials, Arch. Appl. Mech. 72 (2002) pp. 160-170.
- Kwon, S. M., Lee, J. S. and Lee, K. Y., Moving eccentric crack in a piezoelectric strip bonded to two elastic half-planes. Int. J. Solids Struct. 39 (2002), pp. 4395-4406.
- Lee, J. S., Kwon, S. M., Lee, K. Y., and Kwon, J. H., Anti-plane interfacial Yoffe-crack between piezoelectric and two orthotropic layers. Eur. J. Mech. A/Solids 21 (2002), pp. 483-492.
- Ikeda, T., Fundamentals of Piezoelectricity. Oxford University Press, Oxford, UK. (1996).
- Jaffe, B., Cook, Jr. W. R. and Jaffe, H., Piezoelectric Ceramics. Academic Press, London (1996).
- Borrelli, A., Hogan, C. O. and Patria, M. C., Exponential decay of end effects in anti-plane shear for functionally graded piezoelectric materials. Proc. Royal. Soc. London. A 460 (2004), pp. 1193-1212. MR 2133863 (2005k:74032)
- Deng, Wei and Meguid, S. A., Analysis of conducting rigid inclusion at the interface between two dissimilar piezoelectric materials. ASME Journal of Applied Mechanics 65 (1998), pp. 76-83.
- Deeg, W. F., The analysis of dislocation, crack and inclusion problems in piezoelectric solids. Ph. D. Thesis Stanford University, CA, (1980).
- Asundi, A. and Deng, W., Rigid inclusion on the interface between two bonded anisotropic media. J. Mech. Phys. Solids, 43 (1995), pp. 1045-1058
- Chen, T., The rotation of a rigid ellipsoidal inclusion embedded in an anisotropic piezoelectric medium. Int. J. Solids Structures 30 (1993), pp. 1983-1995.
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Additional Information
B. M. Singh
Affiliation:
Department of Computer Science, The University of Calgary, Calgary, Alberta, Canada T2N-1N4
J. Rokne
Affiliation:
Department of Computer Science, The University of Calgary, Calgary, Alberta, Canada T2N-1N4
Email:
rokne@cpsc.ucalgary.ca
R. S. Dhaliwal
Affiliation:
Department of Mathematics and Statistics, The University of Calgary, Calgary, Alberta, Canada T2N-1N4
Email:
dhali.r@shaw.ca
Received by editor(s):
April 14, 2006
Published electronically:
February 12, 2007
Article copyright:
© Copyright 2007
Brown University
