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ANALYSIS OF FREE TORSIONAL VIBRATION IN CARBON NANOTUBES EMBEDDED IN A VISCOELASTIC MEDIUM
(Lublin Univ Technology, Poland, 2015) Arda, Mustafa; Aydogdu, Metin
Carbon Nanotubes (CNTs) have a great potential in many areas like electromechanical systems, medical application, pharmaceutical industry etc. The surrounding physical environment of CNT is very important on torsional vibration behavior of CNT. Damping and elastic effect of medium to the torsional vibration of CNTs are investigated in the present study. Governing equation of motion of nanotube is obtained using Eringen's Nonlocal Elasticty Theory. The effects of some parameters like nonlocal parameter, stiffness parameter and nanotube length are studied in detail.
Axial dynamics of a nanorod embedded in an elastic medium using doublet mechanics
(Elsevier Sci Ltd, 2017) Gul, Ufuk; Aydogdu, Metin; Gaygusuzoglu, Guler
This study investigates the axial vibration of carbon nanotubes (CNTs) embedded in an elastic medium using scale dependent doublet mechanics (DM) theory. Governing equations and all boundary conditions of CNTs are derived based on the variational principle. Free vibration frequencies are obtained and compared with the classical elasticity results for clamped-clamped (C-C) and clamped-free (C-F) boundary conditions. The effect of elastic medium stiffness, nanorod length and doublet separation distance on the axial vibration is examined. It is obtained that important differences exist between vibration frequencies predicted by classical elasticity theory and DM. DM theory can be used in the nano length scale design of structures. (C) 2016 Elsevier Ltd. All rights reserved.
Axial vibration analysis of nanorods (carbon nanotubes) embedded in an elastic medium using nonlocal elasticity
(Pergamon-Elsevier Science Ltd, 2012) Aydogdu, Metin
The axial vibration of single walled carbon nanotube embedded in an elastic medium is studied using nonlocal elasticity theory. The nonlocal constitutive equations of Eringen are used in the formulations. The effect of various parameters like stiffness of elastic medium, boundary conditions and nonlocal parameters on the axial vibration of nanorods is discussed. It is obtained that, the axial vibration frequencies of the embedded nanorods are highly over estimated by the classical continuum rod model which ignores the effect of small length scale. (C) 2012 Elsevier Ltd. All rights reserved.
Axial vibration of carbon nanotube heterojunctions using nonlocal elasticity
(Elsevier Science Bv, 2010) Filiz, Seckin; Aydogdu, Metin
In the present study, axial vibration of carbon nanotube heterojunctions is studied using nonlocal rod theory. The nonlocal constitutive equations of Eringen are used in the formulations. The carbon nanotubes with different lengths, chirality and diameters are considered in the heterojunctions. Effect of nonlocality, length of the carbon nanotubes and lengths of each segment are investigated in detail for each considered problem. It is obtained that, by joining carbon nanotubes good vibrational properties are obtained by suitable selection of parameters. (C) 2010 Elsevier B.V. All rights reserved.
Axial vibration of the nanorods with the nonlocal continuum rod model
(Elsevier, 2009) Aydogdu, Metin
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. (C) 2009 Elsevier B.V. All rights reserved.
Axial Wave Reflection and Transmission in Stepped Nanorods Using Doublet Mechanics Theory
(E D P Sciences, 2018) Aydogdu, Metin; Gul, Ufuk
A numerical investigation of the reflection and transmission of axial waves at stepped nanorods is presented. The scale dependent doublet mechanics theory is used in the analysis. The main difference of the doublet mechanics from other scale dependent models (stress gradient, strain gradient and couple stress theories) is its direct dependence to the micro/nano structure of the solid. Scale parameter is directly related to atomic structure of the material in doublet mechanics theory and it is assumed as carbon-carbon bond length in the present study. However, identification of scale parameters in other scale dependent theories is difficult compared to doublet mechanics theory. Governing equations of stepped nanorods are derived in the framework of doublet mechanics using the Hamilton Principle. The numerical results predicted by doublet mechanics are shown and compared with the classical elasticity.
Bifurcation buckling conditions of FGM plates with different boundaries
(Elsevier Sci Ltd, 2020) Karamanli, Armagan; Aydogdu, Metin
[Abstract Not Available]
Buckling analysis of cross-ply laminated beams with general boundary conditions by Ritz method
(Elsevier Sci Ltd, 2006) Aydogdu, Metin
The present study is concerned with the buckling analysis of cross-ply laminated beams subjected to different sets of boundary conditions. The analysis is based on a three-degree-of-freedom shear deformable beam theory. The requirement of the continuity conditions between layers for symmetric cross-ply laminated beams are satisfied by the use of the shape function incorporated into the theory which also unifies the one-dimensional shear deformable beam theories developed previously. The governing equations are obtained by means of Minimum Energy Principle. Three different combinations of free, clamped and simply supported edge boundary conditions are considered. The critical buckling loads are obtained by applying the Ritz method where the three displacement components are expressed in a series of simple algebraic polynomials. The numerical results were obtained for different length-to-thickness ratios and lay-ups are presented and compared with the ones available in the literature. (c) 2005 Elsevier Ltd. All rights reserved.
Buckling analysis of double nanofibers embeded in an elastic medium using doublet mechanics theory
(ELSEVIER SCI LTD, 2018) Aydogdu, Metin; Gul, Ufuk
This study considers the buckling of double nanofibers embedded in an elastic matrix based on an EulerBernoulli beam model. A scale dependent doublet mechanics theory is used in modelling of the double nanobeam system. Critical buckling loads are obtained using doublet mechanics and results are compared with the classical elasticity theory. The variation of critical buckling loads with different beam length, doublet separation distance and stiffness of the springs are investigated. Some mode shapes of the double nanobeam system are presented.
Buckling analysis of functionally graded beams with periodic nanostructures using doublet mechanics theory
(Springer Heidelberg, 2021) Gul, Ufuk; Aydogdu, Metin
Buckling analysis of functionally graded (FG) nanobeams is examined using doublet mechanics theory. The material properties of FG nanobeams change with the thickness coordinate. A periodic nanostructure model is considered in FG nanobeams which has a simple crystal square lattice type and Euler-Bernoulli beam theory is used in the formulation. Softening or hardening material behaviour has been observed by changing chiral angle of the considered FG periodic nanobeams in the present doublet mechanics theory. Unlike other size dependent theories such as nonlocal stress gradient elasticity theory, couple stress theory, strain gradient theory, this mechanical response (softening or hardening) is seen for the first time in doublet mechanics theory. Mechanical material responses are directly affected by the atomic structure of the considered material in the doublet mechanics theory. Firstly, micro-stress and micro-strain relations are obtained for the considered nanostructure model in doublet mechanics theory. Then, these microequations are transformed to macroequations in the present doublet mechanics theory. Thus, more physical and accurate mechanical results can be obtained in nanostructures using the doublet mechanics theory. After developing the mathematical formulations of FG periodic nanobeams, Ritz method is applied to obtain the critical buckling loads for different boundary conditions. Comparison of example studies with the present doublet mechanics model is presented for verification, and effects of chiral angle on stability response of periodic FG nanobeams are discussed.
Buckling of cross-ply composite plates with linearly varying In-plane loads
(Elsevier Sci Ltd, 2018) Aydogdu, Metin; Aksencer, Tolga
Buckling of composite plates with linearly varying in-plane loads has been studied. Loaded edges are assumed as simply supported and the remaining ones are arbitrary. First order and third order shear deformation plate theories are used in the formulation of the problem. Ritz method has been utilized with simple polynomials in displacement field. By modifying displacement field components, the continuity of transverse stresses is satisfied among the layers of cross-ply symmetric lay-up composite plates. Results are obtained for different material, geometrical properties and loading conditions. (C) 2017 Elsevier Ltd. All rights reserved.
Buckling of laminated composite and sandwich beams due to axially varying in-plane loads
(Elsevier Sci Ltd, 2019) Karamanli, Armagan; Aydogdu, Metin
This paper is dedicated to study the elastic buckling behavior of isotropic, laminated composite and sandwich beams subjected to various axially varying in-plane loads and boundary conditions (BCs). The formulation of the problem is derived by using the Ritz method with the displacement field based on a shear and normal deformable beam theory (SNDBT). Polynomial functions are employed to present the displacement field. The convergence studies are performed and then obtained results are compared with those of reported works. Results from extensive analysis are presented for different BCs, aspect ratios, orthotropy ratios, fiber angles and loading conditions. It is observed that the type of the axially variable in-plane load significantly affects the critical buckling loads and mode shapes of the beams depending on the BCs. The normal deformation effect depends on not only the aspect ratio but also BCs and the fiber orientation angles.
CMC/SWCNT biocomposites: A combined study on experiments, molecular simulations and continuum models
(Elsevier, 2024) Mergen, Omer Bahadir; Gul, Ufuk; Kacar, Gokhan; Arda, Ertan; Aydogdu, Metin
A comprehensive study is carried out including experimental, molecular dynamics (MD) simulations and continuum modelling of Carboxymethyl cellulose/Single walled carbon nanotube (CMC/SWCNT) biocomposites. The electrical, optical, and mechanical properties of CMC/SWCNT biocomposites were investigated in the experimental part of this work. In the result of measurements, it was determined that electrical conductivity (, d c ), absorbance level ( A ) and tensile modulus ( E ) of the composites increased significantly with the increase of SWCNT content in the CMC matrix. These physical changes in the CMC/SWCNT composites were explained by the percolation theory and the electrical and optical percolation thresholds ( R , and R op ) and the critical exponents ( fl , and fl op ) of these composites were calculated. In addition, MD simulations were performed to estimate the material properties for the polymer composite structures. The results of the tensile test experiments were found to qualitatively overlap with the experiments at low concentration range. Moreover, a homogenous distribution of SWCNTs were observed in the CMC matrix together with a strong level of interactions in between. In the continuum modelling a two parameters augmentation model is used. A coupled Mori -Tanaka -self consistent method is utilized when obtaining effective properties of composites. Experimental, MD and continuum modelling results of composites were compared and reasonable agreement was obtained between results.
Comparison of various shear deformation theories for bending, buckling, and vibration of rectangular symmetric cross-ply plate with simply supported edges
(Sage Publications Ltd, 2006) Aydogdu, Metin
In the present study, unified shear deformation theory which was proposed by Soldatos, K.P. and Timarci, T. (1993). A Unified Formulation of Laminated Composite, Shear Deformable Five-degrees-of-freedom Cylindrical Shells on the Basis of a Unified Shear Deformable Shell Theory, Compos. Struct., 25(1-4): 165-171 is used to analyze simply supported symmetric cross-ply rectangular plates for deflections, stresses, natural frequencies, and buckling loads. This theory enables the selection of different in-plane displacement components to represent shear deformation. Exponential shear deformation theory, which is proposed by Karama et al., 40(6) (2003). Mechanical Behavior of Laminated Composite Beam by New Multi-layered Laminated Composite Structures Model with Transverse Shear Stress Continuity, Int J Solids Struct., 40: 1525-1546, is used for the first time to analyze the problem considered. Results which are found by exponential theory are compared with those obtained by using the parabolic shear deformation theory of Reddy, J.N., 51(4) (1984). A Simple Higher-order Theory for Laminated Composite Plates, J Appl Mech., 51: 745-752, the trigonometric shear deformation theory of Touratier, M., 29(8) (1991). An Efficient Standard Plate Theory, Int. Jnl. Engng. Sci., 29(8): 901-916, the hyperbolic shear deformation theory of Soldatos, K.P., 94(3-4) (1992). A Transverse Shear Deformation Theory for Homogeneous Monoclinic Plates, Acta Mech., 94: 1995-220 and with the available three-dimensional elasticity solutions. The study shows that while the transverse displacement and the stresses are best predicted by the exponential shear deformation theory, the parabolic shear deformation and the hyperbolic shear deformation theories yield more accurate predictions for the natural frequencies and the buckling loads.
A comprehensive study on the size-dependent analysis of strain gradient multi-directional functionally graded microplates via finite element model
(Elsevier France-Editions Scientifiques Medicales Elsevier, 2021) Karamanli, Armagan; Aydogdu, Metin; Vo, Thuc P.
This paper presents a comprehensive study on bending, vibration and buckling behaviours of the multi-directional FG microplates. The material properties vary continuously both in-plane and through-thickness directions. Based on a quasi-3D shear and normal deformation plate theory and the modified strain gradient theory, a finite element model is proposed and employed to solve the problems of the multi-directional FG microplates with various boundary conditions. The verification is performed by comparing the numerical results with those from the previous studies. A number of numerical examples on the multi-directional FG microplates with nine boundary conditions and power-law index have been carried out. The effects of three material length scale parameters, aspect ratio, gradient indexes in spatial directions and boundary conditions on the displacements, natural frequencies and buckling loads of 1D, 2D and 3D-FG microplates are investigated in details. Some new results, which are not available in open literature, are provided as references for the future studies. (C) 2021 Elsevier Masson SAS. All rights reserved.
Conditions for functionally graded plates to remain flat under in-plane loads by classical plate theory
(Elsevier Sci Ltd, 2008) Aydogdu, Metin
In this study, conditions for bifurcation buckling of functionally graded plates were investigated by using classical plate theory. Since functionally graded plates were produced generally in an unsymmetrical form with respect to mid-plane, flatness of this type of plate before buckling should be considered as in un-symmetrically laminated composite plates [Leissa, Compos Struct 1986;6:261-70]. It was found that a bending moment is required for simply supported functionally graded plates to remain flat under in-plane loading. Clamped boundary conditions provide the necessary moment conditions. (c) 2006 Elsevier Ltd. All rights reserved.
Developing a novel method to reduce the steering force in heavy trucks
(Inderscience Enterprises Ltd, 2022) Uymaz, Gokay; Aydogdu, Metin
This study investigates the vibration control as a new method for reducing the steering forces and tyre-road friction which occur in steering systems. In this study, the coefficient of friction between the tyre and road, is taken into account as a continuous dynamic and the friction force decreases in the dynamic condition, with the help of controlled vibration. A new system has been designed to replace the so-called drag link in the steering mechanism of commercial vehicles. The draglink replacement part provides controlled vibration for various amplitude and frequency. The new designed system was experimentally verified and then by substituting the experimentally obtained results in the equations, the decrease in the friction coefficient was calculated. Hereby, it has been tried to determine the suitable values of the vibration frequency and amplitude to convert the coefficient of friction between the wheel and the road to the lowest dynamic coefficient of friction. According to the test results, a measurable and significant reduction in steering forces has been determined.
Dynamic analysis of functionally graded beams with periodic nanostructures
(Elsevier Sci Ltd, 2021) Gul, Ufuk; Aydogdu, Metin
It is known from experimental studies that softening or hardening material behaviours of nanostructures change with the microstructure of the considered material. However, most of the size dependent continuum models (nonlocal stress gradient, strain gradient and couple stress theories) predict only softening or hardening material behaviour. Except of these size dependent theories doublet mechanics predicts both softening and hardening responses of the material like experiments in micro/nano-structures. In the present study, free vibration analysis of functionally graded (FG) periodic structure nanobeams are investigated via doublet mechanics theory. Periodic FG nanobeams are modelled as a simple crystal lattice type. Micro strains and stresses are expanded in Taylor series and obtained micro relations transformed to macro stress-strain relations. Thus, by use of bottom-up approach yields the more physical and accurate analysis of nanostructures in the doublet mechanics model. After deriving the mathematical formulation of a periodic FG nanobeam, vibration problem is examined for general boundary conditions. Ritz method is used in the solution. Adjusting of softening and hardening responses of the material gives a beneficial optimization and design of nanostructures.
Dynamic response of a functionally graded tube embedded in an elastic medium due to SH-Waves
(Elsevier, 2018) Kara, Hasan Faik; Aydogdu, Metin
Dynamic response of a cylindrical tube surrounded by an unbounded elastic medium due to plane harmonic SH-Waves is studied. A two-dimensional mathematical model is considered. Cylindrical coordinates are used for convenience. The surrounding medium is assumed to be homogeneous, isotropic and linear elastic. The tube is assumed to be made of linear elastic functionally graded materials (FGMs) such that shear modulus and shear wave velocity are assumed to change linearly from inner surface to outer surface. Material properties are constant along circumferential direction. It is assumed that the inner surface of the tube is traction-free and there is a welded contact between the tube and the surrounding medium. Governing equations are slightly different in the tube region and the unbounded region. Both of the governing equations are solved by applying Finite Fourier Transform in circumferential direction. The exact solution series are presented in terms of Fourier-Bessel series in the unbounded region and power series in the tube region. The presented numerical results show that when the incoming wave lengths decrease, shear stresses at the tube increase significantly. It was shown that for the shorter incoming wave lengths, tubes made of FGMs are subjected to smaller shear stresses compared to the tubes homogeneously made of outer surface material of the FG cases.
Dynamic stability of harmonically excited nanobeams including axial inertia
(Sage Publications Ltd, 2019) Arda, Mustafa; Aydogdu, Metin
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-Poincare 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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