scholarly journals The effect of small scale on the free vibration of functionally graded truncated conical shells

2016 ◽  
Vol 11 (2) ◽  
pp. 91-112 ◽  
Author(s):  
Yaghoub Tadi Beni ◽  
Fahimeh Mehralian
Keyword(s):  
Free Vibration ◽  
Functionally Graded ◽  
Small Scale ◽  
Conical Shells

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.

Free vibration and buckling analysis of elastically supported transversely inhomogeneous functionally graded nanoplate in thermal environment using Rayleigh–Ritz method

2020 ◽  
pp. 107754632096693
Author(s):  
Piyush P Singh ◽  
Mohammad S Azam
Keyword(s):  
Free Vibration ◽  
Thermal Environment ◽  
Ritz Method ◽  
Nonlocal Parameter ◽  
Functionally Graded ◽  
Small Scale ◽  
Pasternak Foundation ◽  
Differential Model ◽  
Aspect Ratios ◽  
Elastically Supported

In this study, free vibration and buckling behaviors of a functionally graded nanoplate supported by the Winkler–Pasternak foundation using a nonlocal classical plate theory are investigated. Eringen’s nonlocal differential model has been used for considering the small-scale effect. The properties of the functionally graded nanoplate are considered to vary transversely following the power law. The governing vibration and buckling equations of an elastically supported functionally graded nanoplate have been derived using the principle of virtual work, and the solution is obtained using the Rayleigh–Ritz method and characteristic polynomials. The advantage of this method is that it disposes of all the drawbacks regarding edge constraints. The objective of the article is to see the effect of edge constraints, aspect ratios, material property exponent, nonlocal parameter, and foundation parameters on the nondimensionalized frequency and the buckling load of an embedded functionally graded nanoplate in a thermal environment. The study highlights that the nonlocal effect is pronounced for higher modes and/or higher aspect ratios and need to be considered for the analysis of the nanoplate. Further, it is observed that the effect of the Pasternak foundation is prominent on nondimensionalized frequencies and buckling of the functionally graded nanoplate.

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