The nonlocal strain gradient approach for torsional vibration of CNTs have been investigated in the present study. The effects of the stress and strain gradient small scale parameters on the non-dimensional frequencies have been obtained.... more
The nonlocal strain gradient approach for torsional vibration of CNTs have been investigated in the present study. The effects of the stress and strain gradient small scale parameters on the non-dimensional frequencies have been obtained. Strain Gradient Theory has stiffening effect on the dynamics of CNT. Combination of both theories gives more acceptable results according to Lattice Dynamics.
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Konferans Bildirisi -- Teorik ve Uygulamalı Mekanik Türk Milli Komitesi, 2008Conference Paper -- Theoretical and Applied Mechanical Turkish National Committee, 2008Bu çalışmada, basit destekli çok duvarlı karbon nanotüplerin titreşimi... more
Konferans Bildirisi -- Teorik ve Uygulamalı Mekanik Türk Milli Komitesi, 2008Conference Paper -- Theoretical and Applied Mechanical Turkish National Committee, 2008Bu çalışmada, basit destekli çok duvarlı karbon nanotüplerin titreşimi genelleştirilmiş kayma deformasyon teorisi kullanılarak incelenmiştir. Çözümlerde parabolik kayma deformasyon teorisi (PKDT) kullanılmıştır. Timoshenko kiriş teorisinden farklı olarak mevcut teori kiriş alt ve üst yüzeyindeki sınır şartlarını sağlar ve böylelikle kayma düzeltme çarpanına gerek yoktur. Serbest titreşim frekansları ve genlik oranları bulunmuş ve önceki çalışmalarla kıyaslanmıştır. Sonuçlar PKDT ile Euler teorisi arasında önemli bir farkın olduğunu göstermektedir. Kayma deformasyonu özellikle yüksek modlar için önem kazanmaktadır.In this study, free vibration of simply supported multi-walled carbon nanotubes (CNTs) was investigated by using the generalized shear deformation-beam theory (GSDBT). Parabolic shear deformation theory (PSDT) is...
First of all Sentilkumar has to be congratulated for his paper [1]. In the paper, the author presented the vibration of double walled carbon nanotubes. He claimed that the equations of motion given in [2] are incorrect. The aim of this... more
First of all Sentilkumar has to be congratulated for his paper [1]. In the paper, the author presented the vibration of double walled carbon nanotubes. He claimed that the equations of motion given in [2] are incorrect. The aim of this communication is to clarify this issue.
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Experimental studies show that softening or hardening behaviors of micro/nanostructures depend on the microstructure of the considered material. Some scale dependent theories like nonlocal elastici...
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Abstract The mechanics of a laminated composite beam attached to inside of a rotating rim and directed to the inward direction is investigated. The Ritz method is utilized in the solution of the problem. Simple algebraic polynomials are... more
Abstract The mechanics of a laminated composite beam attached to inside of a rotating rim and directed to the inward direction is investigated. The Ritz method is utilized in the solution of the problem. Simple algebraic polynomials are used in the displacement field. Clamped-free boundary conditions are considered. First, Reddy (third order) and classical beam theories are used in the formulation. Cross-ply lamination configurations are considered. Effects of rotation speed, hub ratio, orthotropy ratio, beam theory and length to thickness ratio are analyzed in detail. Mode shapes of composite rotating beams are given. It is obtained that composite beams may buckle due to compressive centrifugal force for the some combinations of rotation speed and hub ratio.
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Torsional dynamic analysis of carbon nanotubes under the effect of longitudinal magnetic field is carried out in the present study. Torque effect of an axial magnetic field on a carbon nanotube has been defined using Maxwell’s relation.... more
Torsional dynamic analysis of carbon nanotubes under the effect of longitudinal magnetic field is carried out in the present study. Torque effect of an axial magnetic field on a carbon nanotube has been defined using Maxwell’s relation. Nonlocal governing equation and boundary conditions for carbon nanotubes are obtained by using Hamilton’s minimum energy principle. Eringen’s nonlocal stress gradient elasticity theory is used in the formulation. Fourth order nonlocal equation of motion is solved by utilizing differential quadrature method. Clamped-clamped and clamped-free nonlocal boundary conditions are considered. Nonlocal and axial magnetic field effects on torsional vibration of carbon nanotubes are investigated. The magnetic field has significant effects on the dynamics of carbon nanotubes and may lead to torsional buckling. Critical torsional buckling load reduces with nonlocal effects. Nonlocality shows softening effect on carbon nanotube’s lattice structure. Present results ...
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In the present study, the large deflection of thin inextensible bimodulus functionally graded foam cantilever beams with rectangular cross sections subjected to an end moment at the free end is studied. Ludwick type constitutive material... more
In the present study, the large deflection of thin inextensible bimodulus functionally graded foam cantilever beams with rectangular cross sections subjected to an end moment at the free end is studied. Ludwick type constitutive material properties are assumed. Different stress-strain relations are used in tension and compression domain. Linear Young’s modulus variation is assumed in the thickness direction. Vertical and horizontal deflections of free end and position of neutral surface are given for different material properties. Deflections at the free end for bimodulus cantilevered foam beams can be optimized using functionally grading exponents.
Vibration of axially functionally graded nano-rods and beams is investigated. It is assumed that the material properties change along the rod and beam length. The Ritz method with algebraic polynomials is used in the formulation of the... more
Vibration of axially functionally graded nano-rods and beams is investigated. It is assumed that the material properties change along the rod and beam length. The Ritz method with algebraic polynomials is used in the formulation of the problems. Stress gradient elasticity theory is utilized in order to include the nonlocal effects. Frequencies are obtained for different boundary conditions, geometrical and material properties. Nonlocal parameter is assumed as changing linearly or quadratically along the length of the nanostructure. Frequencies are compared to constant nonlocal parameter cases and considerable differences are observed between constant and variable nonlocal parameter cases. Mode shapes in various cases are depicted in order to explain the effects of axial grading.
This communication aims to initiate an investigation towards understanding the influence that fibre bending stiffness has on the three-dimensional dynamic behaviour of fibrous composites with embedded functionally graded stiff fibres. In... more
This communication aims to initiate an investigation towards understanding the influence that fibre bending stiffness has on the three-dimensional dynamic behaviour of fibrous composites with embedded functionally graded stiff fibres. In this context, it (i) formulates the general dynamical problem of a rectangular plate with embedded a single family of straight fibres that possess bending resistance and are distributed in a controlled, functionally graded manner through the plate thickness, and (ii) for simple support boundary conditions, it solves the free relevant vibration problem. The problem formulation is based on principles of polar linear elasticity and leads to a high-order set of Navier-type partial differential equations with variable coefficients. For simply supported edge boundaries, solution of these equations is achieved with the use of a computationally efficient semi-analytical (so-called fictitious layer) mathematical method. Two types of possible inhomogeneous di...
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Vibration problem of variable cross-sectional nanorods have been investigated. Analytical solutions have been determined for the variable cross-sectional nanorods for a family of cross-sectional variation. Cross-sectional area variation... more
Vibration problem of variable cross-sectional nanorods have been investigated. Analytical solutions have been determined for the variable cross-sectional nanorods for a family of cross-sectional variation. Cross-sectional area variation has been assumed as power function of the axial coordinate. Nonlocal governing equation of motion has been obtained as a second order linear differential equation. Bessel functions have been used in analytical solution of the governing differential equation. Effect of nonlocal and area variation power parameters on dynamics of nanorods have been analyzed. Mode shapes of nanorod have been depicted in various cases and boundary conditions. Present results could be useful at design of atomic force microscope’s probe tip selection.
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Vibration of an axially loaded viscoelastic nanobeam is analyzed in this study. Viscoelasticity of the nanobeam is modeled as a Kelvin-Voigt material. Equation of motion and boundary conditions for viscoelastic nanobeam are provided with... more
Vibration of an axially loaded viscoelastic nanobeam is analyzed in this study. Viscoelasticity of the nanobeam is modeled as a Kelvin-Voigt material. Equation of motion and boundary conditions for viscoelastic nanobeam are provided with help of Eringen’s Nonlocal Elasticity Theory. Initial conditions are used in solution of governing equation of motion. Damping effect of the viscoelastic nanobeam structure is investigated. Nonlocal effect on natural frequency and damping of nanobeam and critical buckling load is obtained.
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This article is concerned with the dynamic stability problem of a nanobeam under a time-varying axial loading. The nonlocal Euler–Bernoulli beam model has been used for the continuum modeling of the nanobeam structure. This problem leads... more
This article is concerned with the dynamic stability problem of a nanobeam under a time-varying axial loading. The nonlocal Euler–Bernoulli beam model has been used for the continuum modeling of the nanobeam structure. This problem leads to a time-dependent Mathieu-Hill equation and has been solved by using the Lindstedt–Poincaré perturbation expansion method. The effect of a small-scale parameter on the dynamic displacement and critical dynamic buckling load of nanobeams has been investigated. Stability regions have been obtained from the local and nonlocal elasticity theories. The effect of the longitudinal vibration of nanobeams on instability regions has been included in the present analysis. Amplitudes of an arbitrary point of a nanobeam due to harmonic loads have been determined. Nonlocal and longitudinal vibration effects reduce the area of the instability region and increase amplitudes.
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In this study, nonlinear wave modulation in nanorods is examined on the basis of nonlocal elasticity theory. Eringen's nonlocal elasticity theory is employed to derive nonlinear equations for the motion of nanorods. The analysis of... more
In this study, nonlinear wave modulation in nanorods is examined on the basis of nonlocal elasticity theory. Eringen's nonlocal elasticity theory is employed to derive nonlinear equations for the motion of nanorods. The analysis of the modulation of axial waves in nonlocal elastic media is performed, and the reductive perturbation method is used for the solution of the nonlinear equations. The propagation of weakly nonlinear and strongly dispersive waves is investigated, and the nonlinear Schrödinger (NLS) equation is acquired as an evolution equation. For the purpose of a numerical investigation of the nonlocal impacts on the NLS equation, it has been investigated whether envelope solitary wave solutions exist by utilizing the physical and geometric features of the carbon nanotubes. Amplitude dependent wave frequencies, phase and group velocities have been obtained and they have compared for the linear local, the linear nonlocal, the nonlinear local and the nonlinear nonlocal c...
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Nonlocal elastic rod model is developed and applied to investigate the small-scale effect on axial vibration of nanorods. Explicit expressions are derived for frequencies for clamped-clamped and clamped-free boundary conditions. It is... more
Nonlocal elastic rod model is developed and applied to investigate the small-scale effect on axial vibration of nanorods. Explicit expressions are derived for frequencies for clamped-clamped and clamped-free boundary conditions. It is concluded that the axial vibration frequencies are highly over estimated by the classical (local) rod model, which ignores the effect of small-length scale. Present results can be used for axial vibration of single-walled carbon nanotubes.
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This study is concerned with the vibration analysis of cross-ply laminated square plates subjected to different sets of boundary conditions. The analysis is based on a five-degree-of-freedom shear deformable plate theory. The requirement... more
This study is concerned with the vibration analysis of cross-ply laminated square plates subjected to different sets of boundary conditions. The analysis is based on a five-degree-of-freedom shear deformable plate theory. The requirement of the continuity conditions among the layers ...
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In this study, free vibration of simply supported multi-walled carbon nanotubes (CNTs) was investigated by using the generalized shear deformation-beam theory (GSDBT). Parabolic shear deformation theory (PSDT) is used in the specific... more
In this study, free vibration of simply supported multi-walled carbon nanotubes (CNTs) was investigated by using the generalized shear deformation-beam theory (GSDBT). Parabolic shear deformation theory (PSDT) is used in the specific solutions. Unlike Timoshenko beam theory present ...
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... Metin Aydogdu* and Seckin Filiz† * Department of Mechanical Engineering, Trakya University 22180, Edirne, Turkey e-mail: metina@trakya.edu.tr † Natural Science Institute, Trakya University, 22180, Edirne, TURKEY Key words: Composite... more
... Metin Aydogdu* and Seckin Filiz† * Department of Mechanical Engineering, Trakya University 22180, Edirne, Turkey e-mail: metina@trakya.edu.tr † Natural Science Institute, Trakya University, 22180, Edirne, TURKEY Key words: Composite plates, Vibration, Attached mass. ...
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The buckling analysis of cross-ply laminated square plates subjected to three types of in-plane forces and various edge boundary conditions is presented on the basis of a unified five-degree-of-freedom shear deformable plate theory. The... more
The buckling analysis of cross-ply laminated square plates subjected to three types of in-plane forces and various edge boundary conditions is presented on the basis of a unified five-degree-of-freedom shear deformable plate theory. The employment of the ...