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Published in: Meccanica 10/2013

01-12-2013

Free vibration of a FGPM circular plate placed in a uniform magnetic field

Authors: Hong-Liang Dai, Ting Dai, Lei Yang

Published in: Meccanica | Issue 10/2013

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Abstract

In this paper, free vibration of a circular plate composed of a transversely isotropic functionally graded piezoelectric material (FGPM) placed in a uniform magnetic field is investigated. Material properties are assumed to depend on the thickness of the circular plate and they are expressed as the same exponential function of h. The problem of free vibration for the transversely isotropic FGPM circular plate with clamped and simply supported boundary conditions is solved by means of the state space method. Numerical examples and some useful discussions are given to demonstrate the significant influence of material inhomogeneity, and adopting a certain value of the graded index can optimize structures of the circular plate. This will be of particular importance in modern engineering design.

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Appendix
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Literature
1.
go back to reference Yang ZG, Zhong Z, Dai Y (2003) Exact solution for axisymmetric free vibration of a functionally graded piezoelectric circular plate. Chin Q Mech 24:506–511 Yang ZG, Zhong Z, Dai Y (2003) Exact solution for axisymmetric free vibration of a functionally graded piezoelectric circular plate. Chin Q Mech 24:506–511
2.
go back to reference Li SR, Fan LL (2007) Free vibration of functionally graded circular plates in thermal environment. J Vib Eng 20:353–360 MathSciNet Li SR, Fan LL (2007) Free vibration of functionally graded circular plates in thermal environment. J Vib Eng 20:353–360 MathSciNet
3.
go back to reference Allahverdizadeh A, Naei MH, Nikkhah BM (2008) Nonlinear free and forced vibration analysis of thin circular functionally graded plates. J Sound Vib 310:966–984 ADSCrossRef Allahverdizadeh A, Naei MH, Nikkhah BM (2008) Nonlinear free and forced vibration analysis of thin circular functionally graded plates. J Sound Vib 310:966–984 ADSCrossRef
4.
go back to reference Allahverdizadeh A, Naei MH, Nikkhah BM (2008) Vibration amplitude and thermal effects on the nonlinear behavior of thin circular functionally graded plates. Int J Mech Sci 50:445–454 CrossRefMATH Allahverdizadeh A, Naei MH, Nikkhah BM (2008) Vibration amplitude and thermal effects on the nonlinear behavior of thin circular functionally graded plates. Int J Mech Sci 50:445–454 CrossRefMATH
5.
go back to reference Nie GJ, Zhong Z (2007) Semi-analytical solution for three-dimensional vibration of functionally graded circular plates. Comput Methods Appl Mech Eng 196:4901–4910 ADSCrossRefMATH Nie GJ, Zhong Z (2007) Semi-analytical solution for three-dimensional vibration of functionally graded circular plates. Comput Methods Appl Mech Eng 196:4901–4910 ADSCrossRefMATH
6.
go back to reference Nie GJ, Zhong Z (2009) Three-dimensional dynamical analysis of functionally graded magnetoelectro-elastic circular plates. J Tongji Univ, Nat Sci 37:749–754 Nie GJ, Zhong Z (2009) Three-dimensional dynamical analysis of functionally graded magnetoelectro-elastic circular plates. J Tongji Univ, Nat Sci 37:749–754
7.
go back to reference Chen WQ, Ding HJ (2002) On free vibration of a functionally graded piezoelectric rectangular plate. Acta Mech 153:207–216 CrossRefMATH Chen WQ, Ding HJ (2002) On free vibration of a functionally graded piezoelectric rectangular plate. Acta Mech 153:207–216 CrossRefMATH
8.
go back to reference Zhang XR, Zhong Z (2005) Three dimensional exact solution for free vibration of functionally gradient piezoelectric circular plate. Chin Q Mech 26:81–86 Zhang XR, Zhong Z (2005) Three dimensional exact solution for free vibration of functionally gradient piezoelectric circular plate. Chin Q Mech 26:81–86
9.
go back to reference Ebrahimi F, Rastgoo A, Kargarnovin MH (2008) Analytical investigation on axisymmetric free vibrations of moderately thick circular functionally graded plate integrated with piezoelectric layers. J Mech Sci Technol 22:1058–1072 CrossRef Ebrahimi F, Rastgoo A, Kargarnovin MH (2008) Analytical investigation on axisymmetric free vibrations of moderately thick circular functionally graded plate integrated with piezoelectric layers. J Mech Sci Technol 22:1058–1072 CrossRef
10.
go back to reference Fu YM, Zhang P (2009) Nonlinear dynamic response of axisymmetric piezoelectric circular plates. Chin J Appl Mech 26:467–472 Fu YM, Zhang P (2009) Nonlinear dynamic response of axisymmetric piezoelectric circular plates. Chin J Appl Mech 26:467–472
11.
go back to reference Wang Y, Xu RQ, Ding HJ (2010) Analytical solutions of functionally graded piezoelectric circular plates subjected to axisymmetric loads. Acta Mech 215:287–305 CrossRefMATH Wang Y, Xu RQ, Ding HJ (2010) Analytical solutions of functionally graded piezoelectric circular plates subjected to axisymmetric loads. Acta Mech 215:287–305 CrossRefMATH
12.
go back to reference Li XY, Wu J, Ding HJ, Chen WQ (2011) 3D analytical solution for a functionally graded transversely isotropic piezoelectric circular plate under tension and bending. Int J Eng Sci 49:664–676 CrossRef Li XY, Wu J, Ding HJ, Chen WQ (2011) 3D analytical solution for a functionally graded transversely isotropic piezoelectric circular plate under tension and bending. Int J Eng Sci 49:664–676 CrossRef
13.
go back to reference Ghorbanpour Arani A, Kolahchi R, Mosallaie Barzoki AA, Loghman A (2012) Electro-thermo-mechanical behaviors of FGPM spheres using analytical method and ANSYS software. Appl Math Model 36:139–157 MathSciNetCrossRefMATH Ghorbanpour Arani A, Kolahchi R, Mosallaie Barzoki AA, Loghman A (2012) Electro-thermo-mechanical behaviors of FGPM spheres using analytical method and ANSYS software. Appl Math Model 36:139–157 MathSciNetCrossRefMATH
14.
go back to reference Dai HL, Jiang HJ, Yang L (2012) Time-dependent behaviors of a FGPM hollow sphere under the coupling of multi-fields. Solid State Sci 14:587–597 CrossRef Dai HL, Jiang HJ, Yang L (2012) Time-dependent behaviors of a FGPM hollow sphere under the coupling of multi-fields. Solid State Sci 14:587–597 CrossRef
15.
go back to reference Xie H, Dai HL, Guo ZY (2012) Dynamic response of a FGPM hollow cylinder under the coupling of multi-fields. Appl Math Comput 218:10492–10499 MathSciNetCrossRefMATH Xie H, Dai HL, Guo ZY (2012) Dynamic response of a FGPM hollow cylinder under the coupling of multi-fields. Appl Math Comput 218:10492–10499 MathSciNetCrossRefMATH
16.
go back to reference Yas MH, Jodaei A, Irandoust S, Nasiri Aghdam M (2012) Three-dimensional free vibration analysis of functionally graded piezoelectric annular plates on elastic foundations. Meccanica 47(6):1401–1423 MathSciNetCrossRef Yas MH, Jodaei A, Irandoust S, Nasiri Aghdam M (2012) Three-dimensional free vibration analysis of functionally graded piezoelectric annular plates on elastic foundations. Meccanica 47(6):1401–1423 MathSciNetCrossRef
17.
go back to reference Dai HL, Dai T, Zheng HY (2012) Stresses distributions in a rotating functionally graded piezoelectric hollow cylinder. Meccanica 47(2):423–436 MathSciNetCrossRef Dai HL, Dai T, Zheng HY (2012) Stresses distributions in a rotating functionally graded piezoelectric hollow cylinder. Meccanica 47(2):423–436 MathSciNetCrossRef
18.
go back to reference Jabbari M, Karampour S, Eslami MR (2013) Steady state thermal and mechanical stresses of a poro-piezo-FGM hollow sphere. Meccanica 48(3):699–719 MathSciNetCrossRef Jabbari M, Karampour S, Eslami MR (2013) Steady state thermal and mechanical stresses of a poro-piezo-FGM hollow sphere. Meccanica 48(3):699–719 MathSciNetCrossRef
19.
go back to reference Sosa HA, Pak YE (1990) Three-dimensional eigenfunction analysis of a crack in a piezoelectric material. Int J Solids Struct 26(1):1–15 CrossRefMATH Sosa HA, Pak YE (1990) Three-dimensional eigenfunction analysis of a crack in a piezoelectric material. Int J Solids Struct 26(1):1–15 CrossRefMATH
20.
go back to reference Ezzat MA (1997) Generation of generalized magnetothermoelastic waves by thermal shock in a perfectly conducting half-space. J Therm Stresses 20(6):633–647 MathSciNetCrossRef Ezzat MA (1997) Generation of generalized magnetothermoelastic waves by thermal shock in a perfectly conducting half-space. J Therm Stresses 20(6):633–647 MathSciNetCrossRef
21.
go back to reference Dai HL, Wang X (2004) Dynamic response of piezoelectric hollow cylinders in an axial magnetic field. Int J Solids Struct 41(18–19):5231–5246 CrossRefMATH Dai HL, Wang X (2004) Dynamic response of piezoelectric hollow cylinders in an axial magnetic field. Int J Solids Struct 41(18–19):5231–5246 CrossRefMATH
22.
go back to reference John KD (1984) Electromagnetic. McGraw-Hill, New York John KD (1984) Electromagnetic. McGraw-Hill, New York
23.
go back to reference Dai HL, Fu YM (2007) Magnetothermoelastic interactions in hollow structures of functionally graded material subjected to mechanical load. Int J Press Vessels Piping 84:132–138 CrossRef Dai HL, Fu YM (2007) Magnetothermoelastic interactions in hollow structures of functionally graded material subjected to mechanical load. Int J Press Vessels Piping 84:132–138 CrossRef
24.
go back to reference Ding HJ, Xu RQ, Chi YW, Chen WQ (1999) Free axisymmetric vibration of transversely isotropic piezoelectric circular plates. Int J Solids Struct 36:4629–4652 CrossRefMATH Ding HJ, Xu RQ, Chi YW, Chen WQ (1999) Free axisymmetric vibration of transversely isotropic piezoelectric circular plates. Int J Solids Struct 36:4629–4652 CrossRefMATH
25.
go back to reference Fan JR (1996) Exact theory of laminated thick plates and shells. Beijing Science, Beijing, pp 111–385 Fan JR (1996) Exact theory of laminated thick plates and shells. Beijing Science, Beijing, pp 111–385
Metadata
Title
Free vibration of a FGPM circular plate placed in a uniform magnetic field
Authors
Hong-Liang Dai
Ting Dai
Lei Yang
Publication date
01-12-2013
Publisher
Springer Netherlands
Published in
Meccanica / Issue 10/2013
Print ISSN: 0025-6455
Electronic ISSN: 1572-9648
DOI
https://doi.org/10.1007/s11012-013-9752-5

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