Free vibration analysis of quadrilateral nanoplates based on nonlocal continuum models using the Galerkin method: the effects of small scale

Meccanica ◽  
2012 ◽  
Vol 48 (4) ◽  
pp. 971-982 ◽  
Author(s):  
H. Babaei ◽  
A. R. Shahidi
Keyword(s):  
Free Vibration ◽  
Galerkin Method ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Continuum Models ◽  
Small Scale ◽  
Nonlocal Continuum ◽  
The Galerkin Method

Free Vibration Analysis of Truncated Conical Composite Shells using the Galerkin Method

2012 ◽  
Vol 12 (7) ◽  
pp. 698-701 ◽  
Author(s):  
Faramarz Ashenai Ghasemi ◽  
Reza Ansari ◽  
Rahim Bakhoday Paskiaby
Keyword(s):  
Free Vibration ◽  
Galerkin Method ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Composite Shells ◽  
The Galerkin Method

Bending, Buckling and Free Vibration Analysis of Size-Dependent Nanoscale FG Beams Using Refined Models and Eringen’s Nonlocal Theory

2020 ◽  
Vol 12 (01) ◽  
pp. 2050007 ◽  
Author(s):  
Atteshamuddin S. Sayyad ◽  
Yuwaraj M. Ghugal
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Volume Fraction ◽  
Constitutive Relations ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Bottom Surface ◽  
Solution Technique ◽  
Small Scale ◽  
Nonlocal Beam

In this study, a theoretical unification of twenty-one nonlocal beam theories are presented by using a unified nonlocal beam theory. The small-scale effect is considered based on the nonlocal differential constitutive relations of Eringen. The present unified theory satisfies traction free boundary conditions at the top and bottom surface of the nanobeam and hence avoids the need of shearing correction factor. Hamilton’s principle is employed to derive the equations of motion. The present unified nonlocal formulation is applied for the bending, buckling and free vibration analysis of functionally graded (FG) nanobeams. The elastic properties of FG material vary continuously by gradually changing the volume fraction of the constituent materials in the thickness direction. Closed-form analytical solutions are obtained by using Navier’s solution technique. Non-dimensional displacements, stresses, natural frequencies and critical buckling loads for FG nanobeams are presented. The numerical results presented in this study can be served as a benchmark for future research.

Sign in / Sign up

Export Citation Format

Share Document