Free vibration analysis of functionally graded rectangular nano-plates considering spatial variation of the nonlocal parameter

Download
2017
Alipour Ghassabi, Ata
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.  

Suggestions

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...
Site Specific Relationship for Strain Dependent Shear Modulus and Damping Using In Situ V S and High Strain Cyclic Test Results
Zehtab, Kaveh Hassan; Yılmaz, Mustafa Tolga (2016-08-18)
This study suggests a practical method for estimating site-specific strain dependent shear modulus and damping. The method uses in-situ shear wave velocity measurements and commercial cyclic laboratory tests on higher strains (i.e., 0.5% to 1%) in which the effect of disturbance is less significant. Shear modulus calculated using in-situ shear wave velocity and at higher cyclic shear strain, is used for building a hyperbolic relationship for shear stress and strain. Modified Masing's rule and the experiment...
Citation Formats
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.