Three-dimensional exact solution for the free vibration of thick functionally graded annular sector plates with arbitrary boundary conditions

Zhao, Jing; Zhang, Yongkang; Choe, Kwangnam; Qu, Xiaofei; Wang, Ailun; Wang, Qingshan

doi:10.1016/j.compositesb.2018.09.107

Cited by 25 publications

(3 citation statements)

References 60 publications

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“…For investigating this subject, various theories (e.g., classical plate theory, 2,3 Mindlin or First-order shear deformation theory, 4,5 third-order shear deformation theory, 6 or 3D elasticity relations 7,8 have been used. Also, there are different methods to solve this subject: numerical, [9][10][11][12] semi-analytical, 13,14 and analytical solution. 15,16 The buckling and thermal buckling analysis of annular sector plates have been studied in different literature.…”

Section: Introductionmentioning

confidence: 99%

Effect of in-plane loads on the natural frequencies of transversely isotropic thick annular sector plates resting on elastic foundation

Baferani

Ohadi

2022

Proceedings of the Institution of Mechanical Engineers, Part C:

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This paper has studied the effects of in-plane load on the vibration of transversely isotropic annular sector plates resting on the Winkler and Pasternak elastic foundations. The governing coupled partial differential equations are obtained based on the third-order shear deformation plate theory. Based on Levy’s solution, the radial edges are assumed to be simply supported, and various boundary conditions are considered for circular edges. Therefore, nine different boundary conditions are considered here. At first, stability equations are analytically solved, and the critical buckling loads are obtained. Then, the natural frequency is extracted from the governing equations of motion subjected to in-plane loads. The effects of different in-plane loads on first natural frequencies of laminated thick annular sector plates with different aspect ratios, various thickness-length ratios, and some Winkler and Pasternak elastic foundation parameters are investigated. In addition, the effects of in-plane load on mode shape contour plots are presented for various boundary conditions. The obtained results show that the in-plane loads have a significant effect on the natural frequency of transversely isotropic annular sector plates. Also, increasing the in-plane force can affect the natural frequencies of the sector plate. For unique industrial designs, the natural frequency of the plate from the work area can be changed or prevent vibrations. Therefore, the resonance phenomenon can be easily changed and modified.

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Section: Introductionmentioning

confidence: 99%

Effect of in-plane loads on the natural frequencies of transversely isotropic thick annular sector plates resting on elastic foundation

Baferani

Ohadi

2022

Proceedings of the Institution of Mechanical Engineers, Part C:

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“…A free vibration behavior analysis of functionally graded sector plates has been presented by Mirtalaie (2018) using a differential quadrature method on the basis of classical plate theory. Zhao et al (2019) obtained an exact solution for the free vibration analysis of thick functionally graded sector plates with arbitrary boundary conditions. The large amplitude thermally induced vibrations of an annular plate have been studied by Javani et al (2019) using a generalized differential quadrature method and a Newmark timemarching scheme in conjunction with the Newton-Raphson method.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Vibration analysis of functionally graded circular plates of variable thickness under thermal environment by generalized differential quadrature method

Lal

Saini

2019

Journal of Vibration and Control

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The vibration of functionally graded circular plates of variable thickness under a thermal environment is analyzed when the nodal lines are concentric circles by using the generalized differential quadrature method for the nonlinear temperature distribution in the thickness direction. The parabolic variation in thickness along the radial direction is controlled by a taper constant. The plate material is graded in the transverse direction and its mechanical properties are temperature-dependent. The thermal environment over the top and bottom surfaces of the plate is assumed to be uniform. Hamilton's principle has been used in obtaining the governing differential equations for thermo-elastic equilibrium and axisymmetric motion for such a plate model employing Kirchhoff plate theory. Numerical results for thermal displacements and natural frequencies of clamped and simply supported plates have been obtained using MATLAB. The effect of the taper constant, volume fraction index, and temperature difference on the vibration characteristics has been analyzed for the lowest three modes of vibration. A study in which the plate material has temperature-independent properties has also been performed. The accuracy of the present technique is verified by comparing the results with those available in the literature.

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Dynamic response of double-FG porous beam system subjected to moving load

Chen

Zhang

Liu

2021

Engineering with Computers

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Three-dimensional exact solution for the free vibration of thick functionally graded annular sector plates with arbitrary boundary conditions

Cited by 25 publications

References 60 publications

Effect of in-plane loads on the natural frequencies of transversely isotropic thick annular sector plates resting on elastic foundation

Effect of in-plane loads on the natural frequencies of transversely isotropic thick annular sector plates resting on elastic foundation

Vibration analysis of functionally graded circular plates of variable thickness under thermal environment by generalized differential quadrature method

Dynamic response of double-FG porous beam system subjected to moving load

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