A nonlocal quasi-3D theory for thermal free vibration analysis of functionally graded material nanoplates resting on elastic foundation

• Published in: Case studies in thermal engineering Vol. 26; p. 101170
• Main Authors: Pham, Quoc-Hoa, Tran, Van Ke, Tran, Trung Thanh, Nguyen-Thoi, Trung, Nguyen, Phu-Cuong, Pham, Van Dong
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.08.2021; Elsevier
• Subjects: Elastic foundation; Finite element method; Free vibration; Functionally graded material; Nanoplates; Nonlocal elasticity theory; Quasi-3D; Finite element method; Elastic foundation; Nanoplates; Free vibration; Functionally graded material; Quasi-3D; Nonlocal elasticity theory
• ISSN: 2214-157X; 2214-157X
• DOI: 10.1016/j.csite.2021.101170

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.