This article presents the free and forced vibration characteristics of an FGPM beam under thermo-electro-mechanical loads using the higher-order shear deformation beam theory. The beam properties are assumed to vary through the thickness direction following the power law distribution in terms of the volume fractions of the constituent materials. The governing equations of motion are derived using Hamilton’s principle. The resulting system of differential equations of vibration is solved using the finite element method. The effects of boundary conditions, material composition, slenderness ratio, mechanical, thermal and electric loading, and transverse shear deformation on natural frequencies and transient response are investigated.
Chen, C.D.2006. ‘‘On the Singularities of the Thermo-Electro-Elastic Fields Near the Apex of a Piezoelectric Bonded Wedge,’’ International Journal of Solids and Structures, 43:957-981.
2.
Hauke, T., Kouvatov, A., Steinhausen, R., Seifert, W., Beige, H., Langhammer, H.T. and Abicht, H.P.2000. ‘‘Bending Behavior of Functionally Gradient Materials,’’ Ferroelectrics, 238:195-202.
3.
Hsu, M.H.2005. ‘‘Electromechanical Analysis of Piezoelectric Laminated Composite Beams,’’ Journal of Marine Science Technology, 13:148-155.
4.
Huang, D.J., Ding, H.J. and Chen, W.Q.2010. ‘‘Static Analysis of Anisotropic Functionally Graded Magneto-Electro-Elastic Beams Subjected to Arbitrary Loading,’’European Journal of Mechanics - A/Solids, 29:356-369.
5.
Kruusing, A.2000. ‘‘Analytical and Optimization of Loaded Cantilever Beam Microactuators,’’ Smart Materials and Structures , 9:186-196.
6.
Lee, H.J.2005. ‘‘Layerwise Laminate Analysis of Functionally Graded Piezoelectric Bimorph Beams,’’ Journal of Intelligent Material Systems and Structures, 16:365-371.
7.
Li, T., Chen, Y.H. and Ma, J.2005. ‘‘Characterization of Fgm Monomorph Actuator Fabricated using Epd,’’ Journal of Material Science , 40:3601-3605.
8.
Li, Y. and Shi, Z.2009. ‘‘Free Vibration of a Functionally Graded Piezoelectric Beam Via State-Space Based Differential Quadrature,’’Composite Structures, 87:257-264.
9.
Liu, T.T. and Shi, Z.F.2004. ‘‘Bending Behavior of Functionally Gradient Piezoelectric Cantilever,’’ Ferroelectrics, 308:43-51.
10.
Lu, C.F. and Chen, W.Q.2005. ‘‘Free Vibration of Orthotropic Functionally Graded Beams with Various End Conditions,’’ Structural Engineering and Mechanics, 13:1430-1437.
11.
Rao, S.S. and Sunar, M.1993. ‘‘Analysis of Distributed Thermopiezoelectric Sensors and Actuators in Advanced Intelligent Structures, ’’ AIAA Journal, 31:1280-1286.
12.
Reddy, J.N.1984a. An Introduction to the Finite Element Method, McGraw-Hill, New York.
13.
Reddy, J.N.1984b. ‘‘A Simple Higher-Order Theory for Laminated Composite Plates,’’ Journal of Applied Mechanics , 51:745-752.
14.
Reddy, J.N.1997. Mechanics of Laminated Composite Plates: Theory and Analysis , CRC Press, New York.
15.
Reddy, J.N. and Chin, C.D.1998. ‘‘Thermo-Mechanical Analysis of Functionally Graded Cylinders and Plates,’’ Journal of Thermal Stresses, 21:593-626.
16.
Saravanos, D.A. and Heyliger, P.R.1999. ‘‘Mechanics and Computational Models for Laminated Piezoelectric Beams, Plates, and Shells,’’ Applied Mechanics Reviews, 52:305-320.
17.
Shi, Z.F.2005. ‘‘Bending Behavior of Piezoelectric Curved Actuator,’’ Smart Materials and Structures, 14:835-842.
18.
Tang, B.2008. ‘‘Combined Dynamic Stiffness Matrix and Precise Time Integration Method for Transient Forced Vibration Response Analysis of Beams,’’ Journal of Sound and Vibration, 309:868-876.
19.
Wu, C.C.M., Kahn, M. and Moy, W.1996. ‘‘Piezoelectric Ceramics With Functional Gradients: A New Application in Material Design,’’Journal of American Ceramic Society, 79:809-812.
20.
Xiang, H.J. and Shi, Z.F.2008. ‘‘Static Analysis for Multi-layered Piezoelectric Cantilevers,’’ International Journal of Solids and Structures, 45:113-128.
21.
Xiang, H.J. and Shi, Z.F.2009. ‘‘Static Analysis for Functionally Graded Piezoelectric Actuators or Sensors Under a Combined Electro-thermal Load,’’European Journal of Mechanics - A/Solids, 28:338-346.
22.
Xiang, H.J. and Yang, J.2008. ‘‘Free and Forced Vibration of a Laminated Fgm Timoshenko Beam of Variable Thickness Under Heat Conduction, ’’ Composites: Part B, 39:292-303.
23.
Yang, J. and Shen, H.S.2002. ‘‘Vibration Characteristics and Transient Response of Shear-deformable Functionally Graded Pates in Thermal Environments ,’’ Journal of Sound and Vibration, 255:579-602.
24.
Yang, J. and Xiang, H.J.2007. ‘‘Thermo-Electro-Mechanical Characteristics of Functionally Graded Piezoelectric Actuators,’’ Smart Materials and Structures, 16:784-797.
25.
Zhang, T.T. and Shi, Z.F.2006. ‘‘Two-dimensional Exact Analyses for Piezoelectric Curved Actuators,’’ Journal of Micromechanics and Microengineering, 16:640-647.
26.
Zhu, X.H. and Meng, Z.1995. ‘‘Operational Principle, Fabrication and Displacement Characteristics of a Functionally Gradient Piezoelectric Ceramic Actuator ,’’ Sensors and Actuators, 48:169-176.
