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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| Published in | Case studies in thermal engineering Vol. 26; p. 101170 |
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| Main Authors | , , , , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.08.2021
Elsevier |
| Subjects | |
| Online Access | Get full text |
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| Abstract | 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. |
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| AbstractList | 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. |
| ArticleNumber | 101170 |
| Author | Pham, Van Dong Nguyen-Thoi, Trung Tran, Van Ke Nguyen, Phu-Cuong Pham, Quoc-Hoa Tran, Trung Thanh |
| Author_xml | – sequence: 1 givenname: Quoc-Hoa orcidid: 0000-0001-6316-3120 surname: Pham fullname: Pham, Quoc-Hoa organization: Advanced Structural Engineering Laboratory, Faculty of Civil Engineering, Ho Chi Minh City Open University, Ho Chi Minh City, Viet Nam – sequence: 2 givenname: Van Ke surname: Tran fullname: Tran, Van Ke organization: Faculty of Mechanical Engineering, Le Quy Don Technical University, Hanoi, Viet Nam – sequence: 3 givenname: Trung Thanh surname: Tran fullname: Tran, Trung Thanh organization: Faculty of Mechanical Engineering, Le Quy Don Technical University, Hanoi, Viet Nam – sequence: 4 givenname: Trung orcidid: 0000-0001-7985-6706 surname: Nguyen-Thoi fullname: Nguyen-Thoi, Trung email: nguyenthoitrung@tdtu.edu.vn organization: Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Viet Nam – sequence: 5 givenname: Phu-Cuong orcidid: 0000-0002-3762-4226 surname: Nguyen fullname: Nguyen, Phu-Cuong email: henycuong@gmail.com, cuong.pn@ou.edu.vn organization: Advanced Structural Engineering Laboratory, Faculty of Civil Engineering, Ho Chi Minh City Open University, Ho Chi Minh City, Viet Nam – sequence: 6 givenname: Van Dong surname: Pham fullname: Pham, Van Dong organization: Department of Management, Military Technical Secondary School, Vinh Phuc, Viet Nam |
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| Keywords | Finite element method Elastic foundation Nanoplates Free vibration Functionally graded material Quasi-3D Nonlocal elasticity theory |
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| Title | A nonlocal quasi-3D theory for thermal free vibration analysis of functionally graded material nanoplates resting on elastic foundation |
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