A nonlocal quasi-3D theory for thermal free vibration analysis of functionally graded material nanoplates resting on elastic foundation
This article proposes a finite element method (FEM) based on a quasi-3D nonlocal theory to study the free vibration of functionally graded material (FGM) nanoplates lying on the elastic foundation (EF) in the thermal environment. By applying Hamilton's principle, the governing equations of FGM...
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2021-08-01
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doaj-a2a780b79b634056afe24055763ccc792021-07-09T04:44:04ZengElsevierCase Studies in Thermal Engineering2214-157X2021-08-0126101170A nonlocal quasi-3D theory for thermal free vibration analysis of functionally graded material nanoplates resting on elastic foundationQuoc-Hoa Pham0Van Ke Tran1Trung Thanh Tran2Trung Nguyen-Thoi3Phu-Cuong Nguyen4Van Dong Pham5Advanced Structural Engineering Laboratory, Faculty of Civil Engineering, Ho Chi Minh City Open University, Ho Chi Minh City, Viet NamFaculty of Mechanical Engineering, Le Quy Don Technical University, Hanoi, Viet NamFaculty of Mechanical Engineering, Le Quy Don Technical University, Hanoi, Viet NamDivision of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Viet Nam; Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, Viet NamAdvanced Structural Engineering Laboratory, Faculty of Civil Engineering, Ho Chi Minh City Open University, Ho Chi Minh City, Viet Nam; Corresponding author.Department of Management, Military Technical Secondary School, Vinh Phuc, Viet NamThis article proposes a finite element method (FEM) based on a quasi-3D nonlocal theory to study the free vibration of functionally graded material (FGM) nanoplates lying on the elastic foundation (EF) in the thermal environment. By applying Hamilton's principle, the governing equations of FGM nanoplates on the EF are obtained. Using the FEM helps solve many complicated problems that analytical solution (AS) cannot be performed yet, such as complex structures, asymmetric problems, variable thickness, etc. The numerical results of this work are compared with those of other published researches to verify accuracy and reliability. In addition, the effects of geometrical parameters, material properties such as the thickness, material exponents, nonlocal coefficients, elastic foundation stiffness, boundary conditions (BCs), and temperature on the free vibration of nanoplates are comprehensively investigated.http://www.sciencedirect.com/science/article/pii/S2214157X21003336Quasi-3DNonlocal elasticity theoryFree vibrationElastic foundationFunctionally graded materialFinite element method |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Quoc-Hoa Pham Van Ke Tran Trung Thanh Tran Trung Nguyen-Thoi Phu-Cuong Nguyen Van Dong Pham |
spellingShingle |
Quoc-Hoa Pham Van Ke Tran Trung Thanh Tran Trung Nguyen-Thoi Phu-Cuong Nguyen Van Dong Pham A nonlocal quasi-3D theory for thermal free vibration analysis of functionally graded material nanoplates resting on elastic foundation Case Studies in Thermal Engineering Quasi-3D Nonlocal elasticity theory Free vibration Elastic foundation Functionally graded material Finite element method |
author_facet |
Quoc-Hoa Pham Van Ke Tran Trung Thanh Tran Trung Nguyen-Thoi Phu-Cuong Nguyen Van Dong Pham |
author_sort |
Quoc-Hoa Pham |
title |
A nonlocal quasi-3D theory for thermal free vibration analysis of functionally graded material nanoplates resting on elastic foundation |
title_short |
A nonlocal quasi-3D theory for thermal free vibration analysis of functionally graded material nanoplates resting on elastic foundation |
title_full |
A nonlocal quasi-3D theory for thermal free vibration analysis of functionally graded material nanoplates resting on elastic foundation |
title_fullStr |
A nonlocal quasi-3D theory for thermal free vibration analysis of functionally graded material nanoplates resting on elastic foundation |
title_full_unstemmed |
A nonlocal quasi-3D theory for thermal free vibration analysis of functionally graded material nanoplates resting on elastic foundation |
title_sort |
nonlocal quasi-3d theory for thermal free vibration analysis of functionally graded material nanoplates resting on elastic foundation |
publisher |
Elsevier |
series |
Case Studies in Thermal Engineering |
issn |
2214-157X |
publishDate |
2021-08-01 |
description |
This article proposes a finite element method (FEM) based on a quasi-3D nonlocal theory to study the free vibration of functionally graded material (FGM) nanoplates lying on the elastic foundation (EF) in the thermal environment. By applying Hamilton's principle, the governing equations of FGM nanoplates on the EF are obtained. Using the FEM helps solve many complicated problems that analytical solution (AS) cannot be performed yet, such as complex structures, asymmetric problems, variable thickness, etc. The numerical results of this work are compared with those of other published researches to verify accuracy and reliability. In addition, the effects of geometrical parameters, material properties such as the thickness, material exponents, nonlocal coefficients, elastic foundation stiffness, boundary conditions (BCs), and temperature on the free vibration of nanoplates are comprehensively investigated. |
topic |
Quasi-3D Nonlocal elasticity theory Free vibration Elastic foundation Functionally graded material Finite element method |
url |
http://www.sciencedirect.com/science/article/pii/S2214157X21003336 |
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