Static and Dynamic Solutions of Functionally Graded Micro/Nanobeams under External Loads Using Non-Local Theory
Abstract
:1. Introduction
2. Modeling and Extraction of Governing Equation
2.1. Formulation of the Problem
2.2. Governing Differential Equations for Functionally Graded (FG) Beam
2.3. Dimensionless Governing Equations in Different Boundary Conditions
3. Static Analysis
4. Buckling Analysis
5. Dynamic Analysis
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Materials | E (GPA) | ρ (kg/m3) |
---|---|---|
Metal (Aluminum) | 70 | 3960 |
Ceramic (Aluminum oxide) | 390 | 2700 |
BCs | k |
---|---|
Simply supported-Simply supported (S-S) | π |
Simply supported-Clamped (S-C) | 4.4934 |
Clamped-Clamped (C-C) | 6.2832 |
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Moheimani, R.; Dalir, H. Static and Dynamic Solutions of Functionally Graded Micro/Nanobeams under External Loads Using Non-Local Theory. Vibration 2020, 3, 51-69. https://doi.org/10.3390/vibration3020006
Moheimani R, Dalir H. Static and Dynamic Solutions of Functionally Graded Micro/Nanobeams under External Loads Using Non-Local Theory. Vibration. 2020; 3(2):51-69. https://doi.org/10.3390/vibration3020006
Chicago/Turabian StyleMoheimani, Reza, and Hamid Dalir. 2020. "Static and Dynamic Solutions of Functionally Graded Micro/Nanobeams under External Loads Using Non-Local Theory" Vibration 3, no. 2: 51-69. https://doi.org/10.3390/vibration3020006