Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
Free vibration analysis of functionally graded rectangular nano-plates considering spatial variation of the nonlocal parameter
Download
index.pdf
Date
2017
Author
Alipour Ghassabi, Ata
Metadata
Show full item record
Item Usage Stats
86
views
26
downloads
Cite This
This study presents a new nonlocal elasticity based analysis method for free vibrations of functionally graded rectangular nano-plates. The method allows taking into account spatial variation of the nonlocal parameter. Governing partial differential equations and associated boundary conditions are derived by employing the variational approach and applying Hamilton’s principle. All required material properties are assumed to be functions of thickness coordinate in the derivations. Displacement field is expressed in a unified way to be able to produce numerical results pertaining to three different plate theories, namely Kirchhoff, Mindlin, and third-order shear deformation theories. The equations are solved numerically by means of the generalized differential quadrature method. Proposed procedures are verified through comparisons made to the results available in the literature. Further numerical results are generated by considering functionally graded simply-supported and cantilever nano-plates undergoing free vibrations. These findings demonstrate influences of factors such as dimensionless plate length, plate theory, nonlocal parameter ratio, and power-law index upon natural vibration frequencies.
Subject Keywords
Elasticity.
,
Vibration.
,
Shear (Mechanics).
URI
http://etd.lib.metu.edu.tr/upload/12620744/index.pdf
https://hdl.handle.net/11511/26258
Collections
Graduate School of Natural and Applied Sciences, Thesis
Suggestions
OpenMETU
Core
Free vibration analysis of functionally graded rectangular nanoplates considering spatial variation of the nonlocal parameter
Ghassabı, A. Alipour; Dağ, Serkan; Ciğeroğlu, Ender (2017-01-01)
WE PRESENT A NEW NONLOCAL ELASTICITY-BASED ANALYSIS METHOD for free vibrations of functionally graded rectangular nanoplates. The introduced method allows taking into account spatial variation of the nonlocal parameter. Governing partial differential equations and associated boundary conditions are derived by employing the variational approach and applying Hamilton's principle. Displacement field is expressed in a unified way to be able to produce numerical results pertaining to three different plate theori...
Frictional Hertzian contact between a laterally graded elastic medium and a rigid circular stamp
Dağ, Serkan; YILDIRIM, BORA; Ozatag, A. Cihan (Springer Science and Business Media LLC, 2013-08-01)
This study investigates the problem of sliding frictional contact between a laterally graded elastic medium and a rigid circular stamp. Analytical and computational methods are developed to evaluate the contact stresses. In the analytical formulation, spatial variation in the shear modulus of the graded medium is represented by an exponential function, and Poisson's ratio is taken as a constant. Coulomb's dry friction law is assumed to hold within the contact area. The two-dimensional plane elasticity probl...
Mixed-mode fracture analysis of orthotropic functionally graded material coatings using analytical and computational methods
Dağ, Serkan (ASME International, 2008-09-01)
This article presents analytical and computational methods for mixed-mode fracture analysis of an orthotropic functionally graded material (FGM) coating-bond coat-substrate structure. The analytical solution is developed by considering an embedded crack in the orthotropic FGM coating. The embedded crack is assumed to be loaded through arbitrary self-equilibrating mixed-mode tractions that are applied to its surfaces. Governing partial differential equations for each of the layers in the trilayer structure a...
New modeling and analysis methods for micro-plates
Aghazadeh, Reza; Dağ, Serkan; Ciğeroğlu, Ender; Department of Mechanical Engineering (2017)
This study presents strain gradient elasticity based procedures for static bending, free vibration and buckling analyses of functionally graded rectangular micro-plates subjected to mechanical and thermal loadings. Mathematically the non-classical modified couple stress and classical elasticity theories are the two special cases of the new model. The methods developed allow taking into account spatial variations of length scale parameters of strain gradient elasticity and modified couple stress theory. Gove...
Thermal stress intensity factor evaluation for inclined cracks in functionally graded materials using Jk-integral method
Demirçivi, Bengi; Dağ, Serkan; Department of Mechanical Engineering (2006)
The main objective of this study is to evaluate mixed mode stress intensity factors for inclined embedded cracks in functionally graded materials. Fracture analysis of inclined cracks requires the calculation of both Mode I and Mode II stress intensity factors ( I K , II K ). In this study, k J -integral is used to calculate I K and II K . Equivalent domain integral approach is utilized to evaluate the k J - integral around the crack tip. The present study aims at developing a finite element model to study ...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
A. Alipour Ghassabi, “Free vibration analysis of functionally graded rectangular nano-plates considering spatial variation of the nonlocal parameter,” M.S. - Master of Science, Middle East Technical University, 2017.
