Three-Dimensional Solution for the Vibration Analysis of Functionally Graded Rectangular Plate with/without Cutouts Subject to General Boundary Conditions

Functionally graded materials (FGMs) structures are increasingly used in engineering due to their superior mechanical and material properties, and the FGMs plate with cutouts is a common structural form, but research on the vibration characteristics of FGMs plate with cutouts is relatively limited....

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Autores principales:	Wenhao Huang, Kai Xue, Qiuhong Li
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	three-dimensional vibration FGMs plate plate with circular cutouts three-dimensional elasticity theory Rayleigh–Ritz method region mapping Technology T Electrical engineering. Electronics. Nuclear engineering TK1-9971 Engineering (General). Civil engineering (General) TA1-2040 Microscopy QH201-278.5 Descriptive and experimental mechanics QC120-168.85
Acceso en línea:	https://doaj.org/article/d7afe2bec15f462fac62092c6c823450
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spelling	oai:doaj.org-article:d7afe2bec15f462fac62092c6c8234502021-11-25T18:16:15ZThree-Dimensional Solution for the Vibration Analysis of Functionally Graded Rectangular Plate with/without Cutouts Subject to General Boundary Conditions10.3390/ma142270881996-1944https://doaj.org/article/d7afe2bec15f462fac62092c6c8234502021-11-01T00:00:00Zhttps://www.mdpi.com/1996-1944/14/22/7088https://doaj.org/toc/1996-1944Functionally graded materials (FGMs) structures are increasingly used in engineering due to their superior mechanical and material properties, and the FGMs plate with cutouts is a common structural form, but research on the vibration characteristics of FGMs plate with cutouts is relatively limited. In this paper, the three-dimensional exact solution for the vibration analysis of FGMs rectangular plate with circular cutouts subjected to general boundary conditions is presented based on the three-dimensional elasticity theory. The displacement field functions are expressed as standard cosine Fourier series plus auxiliary cosine series terms satisfying the boundary conditions in the global coordinate system. The plate with circular cutout is discretized into four curve quadrilateral sub-domains using the <i>p</i>-version method, and then the blending function method is applied to map the closed quadrilateral region to the computational space. The characteristic equation is obtained based on the Lagrangian energy principle and Rayleigh–Ritz method. The efficiency and reliability of proposed method are verified by comparing the present results with those available in the literature and FEM methods. Finally, a parametric study is investigated including the cutout sizes, the cutout positions, and the cutout numbers from the free vibration characteristic analysis and the harmonic analysis. The results can serve as benchmark data for other research on the vibration of FGMs plates with cutouts.Wenhao HuangKai XueQiuhong LiMDPI AGarticlethree-dimensional vibrationFGMs plateplate with circular cutoutsthree-dimensional elasticity theoryRayleigh–Ritz methodregion mappingTechnologyTElectrical engineering. Electronics. Nuclear engineeringTK1-9971Engineering (General). Civil engineering (General)TA1-2040MicroscopyQH201-278.5Descriptive and experimental mechanicsQC120-168.85ENMaterials, Vol 14, Iss 7088, p 7088 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	three-dimensional vibration FGMs plate plate with circular cutouts three-dimensional elasticity theory Rayleigh–Ritz method region mapping Technology T Electrical engineering. Electronics. Nuclear engineering TK1-9971 Engineering (General). Civil engineering (General) TA1-2040 Microscopy QH201-278.5 Descriptive and experimental mechanics QC120-168.85
spellingShingle	three-dimensional vibration FGMs plate plate with circular cutouts three-dimensional elasticity theory Rayleigh–Ritz method region mapping Technology T Electrical engineering. Electronics. Nuclear engineering TK1-9971 Engineering (General). Civil engineering (General) TA1-2040 Microscopy QH201-278.5 Descriptive and experimental mechanics QC120-168.85 Wenhao Huang Kai Xue Qiuhong Li Three-Dimensional Solution for the Vibration Analysis of Functionally Graded Rectangular Plate with/without Cutouts Subject to General Boundary Conditions
description	Functionally graded materials (FGMs) structures are increasingly used in engineering due to their superior mechanical and material properties, and the FGMs plate with cutouts is a common structural form, but research on the vibration characteristics of FGMs plate with cutouts is relatively limited. In this paper, the three-dimensional exact solution for the vibration analysis of FGMs rectangular plate with circular cutouts subjected to general boundary conditions is presented based on the three-dimensional elasticity theory. The displacement field functions are expressed as standard cosine Fourier series plus auxiliary cosine series terms satisfying the boundary conditions in the global coordinate system. The plate with circular cutout is discretized into four curve quadrilateral sub-domains using the <i>p</i>-version method, and then the blending function method is applied to map the closed quadrilateral region to the computational space. The characteristic equation is obtained based on the Lagrangian energy principle and Rayleigh–Ritz method. The efficiency and reliability of proposed method are verified by comparing the present results with those available in the literature and FEM methods. Finally, a parametric study is investigated including the cutout sizes, the cutout positions, and the cutout numbers from the free vibration characteristic analysis and the harmonic analysis. The results can serve as benchmark data for other research on the vibration of FGMs plates with cutouts.
format	article
author	Wenhao Huang Kai Xue Qiuhong Li
author_facet	Wenhao Huang Kai Xue Qiuhong Li
author_sort	Wenhao Huang
title	Three-Dimensional Solution for the Vibration Analysis of Functionally Graded Rectangular Plate with/without Cutouts Subject to General Boundary Conditions
title_short	Three-Dimensional Solution for the Vibration Analysis of Functionally Graded Rectangular Plate with/without Cutouts Subject to General Boundary Conditions
title_full	Three-Dimensional Solution for the Vibration Analysis of Functionally Graded Rectangular Plate with/without Cutouts Subject to General Boundary Conditions
title_fullStr	Three-Dimensional Solution for the Vibration Analysis of Functionally Graded Rectangular Plate with/without Cutouts Subject to General Boundary Conditions
title_full_unstemmed	Three-Dimensional Solution for the Vibration Analysis of Functionally Graded Rectangular Plate with/without Cutouts Subject to General Boundary Conditions
title_sort	three-dimensional solution for the vibration analysis of functionally graded rectangular plate with/without cutouts subject to general boundary conditions
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/d7afe2bec15f462fac62092c6c823450
work_keys_str_mv	AT wenhaohuang threedimensionalsolutionforthevibrationanalysisoffunctionallygradedrectangularplatewithwithoutcutoutssubjecttogeneralboundaryconditions AT kaixue threedimensionalsolutionforthevibrationanalysisoffunctionallygradedrectangularplatewithwithoutcutoutssubjecttogeneralboundaryconditions AT qiuhongli threedimensionalsolutionforthevibrationanalysisoffunctionallygradedrectangularplatewithwithoutcutoutssubjecttogeneralboundaryconditions
_version_	1718411409231970304

Three-Dimensional Solution for the Vibration Analysis of Functionally Graded Rectangular Plate with/without Cutouts Subject to General Boundary Conditions

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