Nonlinear free vibration behavior of functionally graded plates
In this paper, an analytical solution is provided for the nonlinear free vibration behavior of plates made of functionally graded materials. The material properties of the functionally graded plates are assumed to vary continuously through the thickness, according to a power-law distribution of the...
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Published in | Journal of sound and vibration Vol. 289; no. 3; pp. 595 - 611 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
London
Elsevier Ltd
01.01.2006
Elsevier |
Subjects | |
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Abstract | In this paper, an analytical solution is provided for the nonlinear free vibration behavior of plates made of functionally graded materials. The material properties of the functionally graded plates are assumed to vary continuously through the thickness, according to a power-law distribution of the volume fraction of the constituents. The fundamental equations for thin rectangular plates of functionally graded materials are obtained using the von Karman theory for large transverse deflection, and the solution is obtained in terms of mixed Fourier series. The effect of material properties, boundary conditions and thermal loading on the dynamic behavior of the plates is determined and discussed. The results reveal that nonlinear coupling effects play a major role in dictating the fundamental frequency of functionally graded plates. |
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AbstractList | In this paper, an analytical solution is provided for the nonlinear free vibration behavior of plates made of functionally graded materials. The material properties of the functionally graded plates are assumed to vary continuously through the thickness, according to a power-law distribution of the volume fraction of the constituents. The fundamental equations for thin rectangular plates of functionally graded materials are obtained using the von Karman theory for large transverse deflection, and the solution is obtained in terms of mixed Fourier series. The effect of material properties, boundary conditions and thermal loading on the dynamic behavior of the plates is determined and discussed. The results reveal that nonlinear coupling effects play a major role in dictating the fundamental frequency of functionally graded plates. |
Author | Meguid, S.A. Ong, L.S. Woo, J. |
Author_xml | – sequence: 1 givenname: J. surname: Woo fullname: Woo, J. organization: Engineering Mechanics and Design Laboratory, Department of Mechanical and Industrial Engineering, University of Toronto, 5 King's College Road, Toronto, Ontario, Canada M5S 3G8 – sequence: 2 givenname: S.A. surname: Meguid fullname: Meguid, S.A. email: meguid@mie.utoronto.ca organization: Engineering Mechanics and Design Laboratory, Department of Mechanical and Industrial Engineering, University of Toronto, 5 King's College Road, Toronto, Ontario, Canada M5S 3G8 – sequence: 3 givenname: L.S. surname: Ong fullname: Ong, L.S. organization: Engineering Mechanics Division, School of Mechanical and Production Engineering, Nanyang Technological University, 50 Nanyang Avenue 639798, Singapore |
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Keywords | High strain Volume fraction Free vibration Thin plate Thermomechanical properties Fourier series Modeling Natural frequency Thermal properties Edge effect Functionnally graded material Rectangular plate Von Kárman equation Non linear effect Power law Dynamic load |
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References | Wetherhold, Seelman, Wang (bib4) 1996; 56 Miyamoto (bib9) 1999 Ishikawa (bib2) 1990 Ichikawa (bib6) 2000 Takezono, Tao, Inamura, Inoue (bib3) 1996; 39 Nayfeh, Mook (bib10) 1979 Praveen, Reddy (bib7) 1998; 35 Tanaka, Tanaka, Watanabe, Poterasu, Sugano (bib1) 1993; 109 Woo, Meguid (bib5) 2001; 38 Loy, Lam, Reddy (bib8) 1999; 41 Takezono (10.1016/j.jsv.2005.02.031_bib3) 1996; 39 Praveen (10.1016/j.jsv.2005.02.031_bib7) 1998; 35 Loy (10.1016/j.jsv.2005.02.031_bib8) 1999; 41 Miyamoto (10.1016/j.jsv.2005.02.031_bib9) 1999 Wetherhold (10.1016/j.jsv.2005.02.031_bib4) 1996; 56 Woo (10.1016/j.jsv.2005.02.031_bib5) 2001; 38 Tanaka (10.1016/j.jsv.2005.02.031_bib1) 1993; 109 Nayfeh (10.1016/j.jsv.2005.02.031_bib10) 1979 Ichikawa (10.1016/j.jsv.2005.02.031_bib6) 2000 Ishikawa (10.1016/j.jsv.2005.02.031_bib2) 1990 |
References_xml | – volume: 38 start-page: 7409 year: 2001 end-page: 7421 ident: bib5 article-title: Nonlinear behaviour of functionally graded plates and shallow shells publication-title: International Journal of Solids and Structures contributor: fullname: Meguid – year: 2000 ident: bib6 article-title: Functional Graded Materials in the 21st Century contributor: fullname: Ichikawa – volume: 109 start-page: 377 year: 1993 end-page: 389 ident: bib1 article-title: Improved solution to thermoelastic material design in functionally graded materials: scheme to reduce thermal stresses publication-title: Computer Methods in Applied Mechanics and Engineering contributor: fullname: Sugano – year: 1979 ident: bib10 article-title: Nonlinear Oscillations contributor: fullname: Mook – volume: 39 start-page: 573 year: 1996 end-page: 581 ident: bib3 article-title: Thermal stress and deformation in functionally graded material shells of revolution under thermal loading due to fluid publication-title: JSME International Journal Series A: Mechanics and Material Engineering contributor: fullname: Inoue – volume: 41 start-page: 309 year: 1999 end-page: 324 ident: bib8 article-title: Vibration of functionally graded cylindrical shells publication-title: International Journal of Mechanical Science contributor: fullname: Reddy – start-page: 11 year: 1990 end-page: 25 ident: bib2 article-title: Thermal deformation and thermal stress of FGM plates under steady graded temperature field publication-title: Proceedings of the First International Symposium on FGM contributor: fullname: Ishikawa – volume: 35 start-page: 4457 year: 1998 end-page: 4476 ident: bib7 article-title: Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates publication-title: International Journal of Solids and Structures contributor: fullname: Reddy – year: 1999 ident: bib9 article-title: Functional Graded Materials: Design, Processing and Applications contributor: fullname: Miyamoto – volume: 56 start-page: 1099 year: 1996 end-page: 1104 ident: bib4 article-title: Use of functionally graded materials to eliminate or control thermal deformation publication-title: Composites Science and Technology contributor: fullname: Wang – volume: 41 start-page: 309 year: 1999 ident: 10.1016/j.jsv.2005.02.031_bib8 article-title: Vibration of functionally graded cylindrical shells publication-title: International Journal of Mechanical Science doi: 10.1016/S0020-7403(98)00054-X contributor: fullname: Loy – start-page: 11 year: 1990 ident: 10.1016/j.jsv.2005.02.031_bib2 article-title: Thermal deformation and thermal stress of FGM plates under steady graded temperature field contributor: fullname: Ishikawa – volume: 35 start-page: 4457 year: 1998 ident: 10.1016/j.jsv.2005.02.031_bib7 article-title: Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates publication-title: International Journal of Solids and Structures doi: 10.1016/S0020-7683(97)00253-9 contributor: fullname: Praveen – volume: 109 start-page: 377 year: 1993 ident: 10.1016/j.jsv.2005.02.031_bib1 article-title: Improved solution to thermoelastic material design in functionally graded materials: scheme to reduce thermal stresses publication-title: Computer Methods in Applied Mechanics and Engineering doi: 10.1016/0045-7825(93)90088-F contributor: fullname: Tanaka – year: 1999 ident: 10.1016/j.jsv.2005.02.031_bib9 contributor: fullname: Miyamoto – volume: 39 start-page: 573 year: 1996 ident: 10.1016/j.jsv.2005.02.031_bib3 article-title: Thermal stress and deformation in functionally graded material shells of revolution under thermal loading due to fluid publication-title: JSME International Journal Series A: Mechanics and Material Engineering contributor: fullname: Takezono – year: 2000 ident: 10.1016/j.jsv.2005.02.031_bib6 contributor: fullname: Ichikawa – volume: 56 start-page: 1099 year: 1996 ident: 10.1016/j.jsv.2005.02.031_bib4 article-title: Use of functionally graded materials to eliminate or control thermal deformation publication-title: Composites Science and Technology doi: 10.1016/0266-3538(96)00075-9 contributor: fullname: Wetherhold – volume: 38 start-page: 7409 year: 2001 ident: 10.1016/j.jsv.2005.02.031_bib5 article-title: Nonlinear behaviour of functionally graded plates and shallow shells publication-title: International Journal of Solids and Structures doi: 10.1016/S0020-7683(01)00048-8 contributor: fullname: Woo – year: 1979 ident: 10.1016/j.jsv.2005.02.031_bib10 contributor: fullname: Nayfeh |
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