Nonlinear free vibration of pre- and post-buckled FGM plates on two-parameter foundation in the thermal environment

Taczała, Maciej; Buczkowski, Ryszard; Kleiber, Michał

doi:10.1016/j.compstruct.2015.11.017

Cited by 17 publications

(4 citation statements)

References 19 publications

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“…The geometrically nonlinear vibration characteristics of thermally postbuckled isotropic/ anisotropic laminated plates were studied by Yang and Han (1983), Librescu et al (1996aLibrescu et al ( , 1996b, Librescu and Lin (1997), Lee (1997a, 1997b), Oh et al (2000), Ramachandra (2005a, 2005b), Fazzolari and Carrera (2013) and Samadpour et al (2015). Thermally postbuckled plates made of functionally graded (FG) metal/ceramic composite were studied by Park and Kim (2006), Xia and Shen (2008), and Taczala et al (2016), whereas thermally postbuckled plates made of FG carbon nanotube-reinforced composite (CNTRC) were investigated recently by Fan and Wang (2016), Shen and Wang, (2017), and Fazzolari (2018). A comprehensive survey of these studies can be found in Shen and Wang (2017).…”

Section: Introductionmentioning

confidence: 99%

“…(2015). Thermally postbuckled plates made of functionally graded (FG) metal/ceramic composite were studied by Park and Kim (2006), Xia and Shen (2008), and Taczala et al. (2016), whereas thermally postbuckled plates made of FG carbon nanotube-reinforced composite (CNTRC) were investigated recently by Fan and Wang (2016), Shen and Wang, (2017), and Fazzolari (2018).…”

Section: Introductionmentioning

confidence: 99%

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Vibration of thermally postbuckled FG-GRC laminated plates resting on elastic foundations

Shen

Xiang

Fan

2019

Journal of Vibration and Control

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This paper investigates the small-and large-amplitude vibrations of thermally postbuckled graphene-reinforced composite (GRC) laminated plates resting on elastic foundations. The piecewise GRC layers are arranged in a functionally graded (FG) pattern along the thickness direction of the plate. The anisotropic and temperature-dependent material properties of the FG-GRC layers are estimated through the extended Halpin-Tsai micromechanical model. Based on the Reddy's higher order shear deformation plate theory and the von Kármán strain-displacement relationships, the motion equations of the plates are derived. The foundation support, the thermal effect, and the initial deflection caused by thermal postbuckling are also included in the derivation. A two-step perturbation approach is applied to determine the thermal postbuckling equilibrium paths as well as the nonlinear vibration solutions for the FG-GRC laminated plates. The numerical illustrations concern small-and large-amplitude vibration characteristics of thermally postbuckled FG-GRC laminated plates under a uniform temperature field. The effects of graphene reinforcement distributions and foundation stiffnesses on the vibration responses of FG-GRC laminated plates are examined in detail.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Vibration of thermally postbuckled FG-GRC laminated plates resting on elastic foundations

Shen

Xiang

Fan

2019

Journal of Vibration and Control

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“…Mindlin’s and Reissner’s theories take into consideration the effect of shear stresses across the thickness of the plate and require the use of correctional factors which generally depend on the shape and geometry. FSDT theory has been widely used in numerous papers mainly for solving nonlinear problems [22,23]. Static problems due to introducing geometric nonlinearity have been studied in [24], using Green’s strain tensor, and in [25] using von Karman’s strain tensor.…”

Section: Introductionmentioning

confidence: 99%

New Shape Function for the Bending Analysis of Functionally Graded Plate

Čukanović¹,

Radaković

Bogdanović

et al. 2018

Materials

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The bending analysis of thick and moderately thick functionally graded square and rectangular plates as well as plates on Winkler–Pasternak elastic foundation subjected to sinusoidal transverse load is presented in this paper. The plates are assumed to have isotropic, two-constituent material distribution through the thickness, and the modulus of elasticity of the plate is assumed to vary according to a power-law distribution in terms of the volume fractions of the constituents. This paper presents the methodology of the application of the high order shear deformation theory based on the shape functions. A new shape function has been developed and the obtained results are compared to the results obtained with 13 different shape functions presented in the literature. Also, the validity and accuracy of the developed theory was verified by comparing those results with the results obtained using the third order shear deformation theory and 3D theories. In order to determine the procedure for the analysis and the prediction of behavior of functionally graded plates, the new program code in the software package MATLAB has been developed based on the theories studied in this paper. The effects of transversal shear deformation, side-to-thickness ratio, and volume fraction distributions are studied and appropriate conclusions are given.

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“…Further, they presented nonlinear free vibration analysis of functionally graded beam resting on nonlinear elastic foundation using Galerkin one-parameter solution with von-Karman's strain displacement relation [18]. Taczala et al [19] investigated the geometric nonlinear free vibration of the thick FGM plate in the thermal environment that is supported on a two-parameter foundation using FSDT and von Karman nonlinearity. Yang et al [20] obtained the theoretical solution for a rectangular plate resting on elastic foundation with free edges by a reciprocal theorem method.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear free vibration analysis of functionally graded plate resting on elastic foundation in thermal environment using higher order shear deformation theory

Parida

Mohanty

2018

Scientia Iranica

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This paper deals with nonlinear vibration analysis of a functionally graded plate resting on Pasternak elastic foundation in a thermal environment. A mathematical model is developed based on a higher-order shear deformation theory using Green-Lagrange type nonlinearity. The model includes all the nonlinear terms to obtain a general form and to present the original exure of the plate. The material properties are considered as temperature dependent and graded along thickness direction following a simple power law distribution in terms of volume fraction of the constituents. The compression/traction free condition is employed to obtain a simpli ed model with seven parameters instead of nine parameters. The plate model has been discretized into C 0 eight-noded quadratic elements with seven degrees of freedom per node. The governing equation of the functionally graded plate has been derived using Hamilton's principle and solved by a direct iterative method. The present model is validated by comparing the obtained results with those published in the literature. The e ects of volume fraction index, aspect ratio, thickness ratio, support conditions, elastic foundation modulus, and temperature on the nonlinear frequencies of the functionally graded plates are discussed. It has been found that the intermediate material property does not necessarily give intermediate nonlinear frequency.

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Nonlinear free vibration of pre- and post-buckled FGM plates on two-parameter foundation in the thermal environment

Cited by 17 publications

References 19 publications

Vibration of thermally postbuckled FG-GRC laminated plates resting on elastic foundations

Vibration of thermally postbuckled FG-GRC laminated plates resting on elastic foundations

New Shape Function for the Bending Analysis of Functionally Graded Plate

Nonlinear free vibration analysis of functionally graded plate resting on elastic foundation in thermal environment using higher order shear deformation theory

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