Elastic Solutions of Graded Piezoelectric Hollow Cylinders


Article Preview

In the present paper, two kinds of thick-walled hollow cylinders are studied. One is the cylinder with multi-layers and another is functionally graded cylinder. Both the cylinders are made of piezoelectric materials. Based on the basic piezoelectric equations, the exact solutions for the elastic hollow cylinder with N-layers submitted to external voltage are obtained. For the graded hollow cylinder the exact solutions are obtained by using displacement method and three hypergeometric functions. Comparisons demonstrate that the limitation of the multilayer cases is consistent with that of graded cases.



Key Engineering Materials (Volumes 302-303)

Edited by:

Nai-Qian Feng and Gai-Fei Peng




Z. Shi and T. T. Zhang, "Elastic Solutions of Graded Piezoelectric Hollow Cylinders", Key Engineering Materials, Vols. 302-303, pp. 658-668, 2006

Online since:

January 2006




[1] Parton V Z and and Kudryavtsev B A: Electromagnetoelastricity (New York: Gordon and Breach 1988).

[2] Olesiak Z S and. Pyryev Y U A: A Coupled Quasi-stationary Problem of Thermodiffusion for An Elastic Cylinder. Journal of Engineering Science, 1995, 33(6), pp.773-780.

DOI: https://doi.org/10.1016/0020-7225(94)00099-6

[3] Rajapakse R K N D and Zhou Y: Stress analysis of piezoceramic cylinders. Smart Mater. Struct. 1997, 6, pp.169-177.

[4] Ting T C T: Pressuring, shearing, torsion and extension of a circular tube or bar of a cylindrically anisotropic material. Proc. R. Soc. Lond. 1996, A452, pp.2397-2421.

DOI: https://doi.org/10.1098/rspa.1996.0129

[5] Ting T C T: New solutions to pressuring, shearing, torsion and extension of a circular tube or bar. Proc. R. Soc. Lond. 1999, A455, pp.3527-3542.

[6] Chen, T, Chung, C T & Lin, W L: A revisit of a cylindrically anisotropic tube subjected to pressuring, shearing, torsion, extension, and a uniform change. Int. J. Solids Struct. 2000, 37, pp.5143-5159.

DOI: https://doi.org/10.1016/s0020-7683(99)00202-4

[7] Valle Christine, Qu Jianming, Jacbos Laurence J : Guided Circumferential Waves in Layered Cylinders. International Journal of Engineering Science, 1999, 37, pp.1369-1387.

DOI: https://doi.org/10.1016/s0020-7225(98)00133-5

[8] Tran Jiang-Quo: Exact solutions of a piezoelectric circular tube or bar under extension, torsion, pressing, shearing, uniform electric loading and temperature change. Proc. R. Soc. Lond. 2002, A 458, pp.2349-2367.

DOI: https://doi.org/10.1098/rspa.2002.0969

[9] Alshits V I and Kirchner H K: Cylindrically anisotropic, radically inhomogeneous elastic material. Proc. R. Soc. Lond. 2001, A457, pp.671-693.

[10] Shi Zhifei: General solution of a density functionally gradient piezoelectric cantilever and its applications. Smart Materials and Structures, 2002, 11(1), pp.122-129.

DOI: https://doi.org/10.1088/0964-1726/11/1/314

[11] Shi Zhifei and Chen Ying: Functionally graded piezoelectric cantilever beam under load. Archive of Applied Mechanics, 2004, 74, pp.237-247.

DOI: https://doi.org/10.1007/s00419-004-0346-5

[12] Leissa A 1993 Vibration of plates, Reprint Acoustical Society of America.

[13] Hung-Ming Cheng, Michael T S Ewe1, George T-C Chiu and Rashid Bashir: Modeling and control of piezoelectric cantilever beam micro-mirror and micro-laser arrays to reduce image banding in electrophotographic processes J. Micromech. Microeng. 11 (2001).

DOI: https://doi.org/10.1088/0960-1317/11/5/307

[14] Michel Brissaud 2004 Modelling of non-symmetric piezoelectric bimorphs J. Micromech. Microeng. 14, pp.1507-1518.

DOI: https://doi.org/10.1088/0960-1317/14/11/011

[15] McMahon G W: The ring-shell flextensional transducer (class v), in power transducers for sonics and ultrasonics, Hamonic B F, Wilson OB, Decarpigny J N, eds. Berlins, Heideberg: Springer-verla, 1991, pp.60-74.

DOI: https://doi.org/10.1007/978-3-642-76271-0_7

[16] Berlincourt D: Piezoelectric crystals and ceramics in ultrasonic transducer materials, Mattiat O E, ed. New York: Plenum press, (1971).

[17] Rogers P H: Mathematical model for a free-flooded piezoelectric cylinder. J Acoust Soc Am. 1986, 1(80), pp.13-17.

[18] Kielczynski P, Pajewski W, Szalewski M: Piezoelectric sensors for investigations of microstructures. Sensors and Actuators 1998, A65, pp.13-18.

DOI: https://doi.org/10.1016/s0924-4247(98)80003-4