Dynamic stability of functionally graded nanobeam based on nonlocal Timoshenko theory considering surface effects

2017 ◽  
Vol 520 ◽  
pp. 97-105 ◽  
Author(s):  
Shahab Saffari ◽  
Mohammad Hashemian ◽  
Davood Toghraie
Keyword(s):  
Dynamic Stability ◽  
Surface Effects ◽  
Functionally Graded ◽  
Timoshenko Theory ◽  
Functionally Graded Nanobeam

Dynamic stability/instability simulation of the rotary size-dependent functionally graded microsystem

2021 ◽  
Author(s):  
Xiaoping Huang ◽  
Huadong Hao ◽  
Khaled Oslub ◽  
Mostafa Habibi ◽  
Abdelouahed Tounsi
Keyword(s):  
Dynamic Stability ◽  
Functionally Graded ◽  
Size Dependent

Nonlinear Vibration Analysis of Functionally Graded Nanobeam Using Homotopy Perturbation Method

2016 ◽  
Vol 9 (1) ◽  
pp. 144-156 ◽  
Author(s):  
Majid Ghadiri ◽  
Mohsen Safi
Keyword(s):  
Differential Equation ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Partial Differential Equation ◽  
Beam Theory ◽  
Nonlocal Elasticity Theory ◽  
Functionally Graded ◽  
Simply Supported ◽  
Homotopy Perturbation ◽  
Functionally Graded Nanobeam

AbstractIn this paper, He's homotopy perturbation method is utilized to obtain the analytical solution for the nonlinear natural frequency of functionally graded nanobeam. The functionally graded nanobeam is modeled using the Eringen's nonlocal elasticity theory based on Euler-Bernoulli beam theory with von Karman nonlinearity relation. The boundary conditions of problem are considered with both sides simply supported and simply supported-clamped. The Galerkin's method is utilized to decrease the nonlinear partial differential equation to a nonlinear second-order ordinary differential equation. Based on numerical results, homotopy perturbation method convergence is illustrated. According to obtained results, it is seen that the second term of the homotopy perturbation method gives extremely precise solution.

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