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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 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.
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.
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.
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 analysis of short-fiber reinforced composite nanobeams based on nonlocal strain gradient theory
(Sage Publications Ltd, 2024) Gul, Ufuk
This study deals with the dynamic behavior of short-fiber reinforced composite nanobeams. It is assumed that short-fibers are aligned or randomly distributed in the composite nanobeams. Nonlocal strain gradient theory is applied to composite nanobeam mechanics including Euler-Bernoulli and Timoshenko beam models. The transverse vibration of these composite nanobeams is investigated for various boundary conditions. Approximate Ritz method is used for obtaining the natural frequencies of short-fiber reinforced composite nanobeams. In addition to vibration analysis, wave propagation in short-fiber reinforced composite nanobeams is investigated and wave dispersion relations are analytically obtained for both Euler-Bernoulli and Timoshenko beam models. The vibration and wave dispersion results of short-fiber reinforced composite nanobeams are obtained for aligned and randomly distributed cases. The results obtained from this paper showed that there is no significant difference between the aligned and randomly oriented short-fiber composite nanobeams. This provides great convenience to designers where it is not possible to orient the reinforcement material in composites. The present study may be useful for the mechanical analysis and design of micro/nano-electromechanical systems (MEMS/NEMS), nanoprobes, nanosensors, nanoactuators, and atomic force microscopes.
Dynamics of a functionally graded Timoshenko beam considering new spectrums
(Elsevier Sci Ltd, 2019) Gul, Ufuk; Aydogdu, Metin; Karacam, Fatih
Dynamics of a functionally graded (FG) beam were studied using Timoshenko and Euler-Bernoulli (EB) beam theories. Wave propagation of infinite beams and vibration analysis of simply supported FG beams were investigated. Variation of the material properties were assumed in the power law form. It was obtained that unlike isotropic beams, axial and transverse waves are coupled in FG beams due to unsymmetric material variation in the thickness direction of the beam. Two and three dispersion curves were obtained for EB and Timoshenko beam theory, respectively. All of these modes are axial-flexural coupled modes and coupling degree depends on material distribution with respect to mid-surface of the beam. The spectrums of different beams may be classified considering corresponding mode shapes. Wave propagation and vibration properties were discussed considering their mode shapes. It is seen that, unlike isotropic beams, pure shear mode is not possible for FG beams.
Finite element analysis for longitudinal vibration of nanorods based on doublet mechanics
(Techno-Press, 2023) Gul, Ufuk; Aydogdu, Metin
In the present study, the axial vibration of the nanorods is investigated in the framework of the doublet mechanics theory. The equations of motion and boundary conditions of nanorods are derived by applying the Hamilton principle. A finite element method is developed to obtain the vibration frequencies of nanorods for different boundary conditions. A two-noded higher order rod finite element is used to solve the vibration problem. The natural frequencies of nanorods obtained with the present finite element analysis are validated by comparing the results of classical doublet mechanics and nonlocal strain gradient theories. The effects of rod length, mode number and boundary conditions on the axial vibration frequencies of nanorods are examined in detail. Mode shapes of the nanorods are presented for the different boundary conditions. It is shown that the doublet mechanics model can be used for the dynamic analysis of nanotubes, and the presented finite element formulation can be used for mechanical problems of rods with unavailable analytical solutions. These new results can also be used as references for the future studies.
Longitudinal vibration of Bishop nanorods model based on nonlocal strain gradient theory
(Springer Heidelberg, 2022) Gul, Ufuk; Aydogdu, Metin
In this study, the longitudinal vibration of nanorods is investigated in the framework of nonlocal strain gradient theory and Bishop's rod model for the first time in the literature. Unlike simple rod theory, radial deformation and radial inertia are considered in Bishop rod theory. After deriving the kinematic relations of this Bishop nanorod model, Ritz method is used in order to determine the natural frequencies for different boundary conditions. It is obtained that the nonlocal strain gradient theory predicts the softening or hardening material behaviour compared to classical Bishop rod theory depending on the magnitude of the material length scale parameter and nonlocal parameter. This mechanical behaviour can provide a favourable design of nano/micro-scale structures. To show the validation of this study, natural frequencies calculated by using the present nonlocal strain gradient model are compared to results of other nonlocal strain gradient models in the literature and good agreement has been observed. The dimensionless frequencies of Bishop nanorod model are obtained by using the nonlocal strain gradient theory for different parameters such as material length scale parameter, nonlocal parameter, nanorod length, radius of gyration and mode number and a comprehensive review is executed in the numerical results.
Longitudinal vibration of double nanorod systems using doublet mechanics theory
(Techno-Press, 2020) Aydogdu, Metin; Gul, Ufuk
This paper investigates the free and forced longitudinal vibration of a double nanorod system using doublet mechanics theory. The doublet mechanics theory is a multiscale theory spanning between lattice dynamics and continuum mechanics. Equations of motion and boundary conditions for the double nanorod system are obtained using Hamilton's principle. Clamped-clamped and clamped-free boundary conditions are considered. Frequencies and dynamic displacements are determined to demonstrate the effects of length scale parameter of considered material and geometry of the nanorods. It is shown that frequencies obtained by the doublet mechanics theory are bounded from above (van Hove singularity) and unlike classical elasticity theory doublet mechanics theory predicts finite number of modes depending on the length of the nanotube. The present doublet mechanics results have been compared to molecular dynamics, experimental and nonlocal theory results and good agreement is observed between the present and other mentioned results. The difference between wave frequencies of graphite is less than 10% between doublet mechanics and experimental results near to the end of the first Brillouin zone.
A micro/nano-scale Timoshenko-Ehrenfest beam model for bending, buckling and vibration analyses based on doublet mechanics theory
(Elsevier, 2021) Gul, Ufuk; Aydogdu, Metin
A micro-nano-scale Timoshenko-Ehrenfest beam model is investigated using doublet mechanics theory in the present study. The governing equations and all possible boundary conditions are obtained based on doublet mechanics model. The static bending, buckling and vibration problems of Timoshenko microbeams are examined in detail. Deflection, rotation, critical buckling loads and natural frequencies predicted by the present doublet mechanics model are obtained for simply supported micro-scale Timoshenko beams by the Navier solution method. The obtained results are compared to other classical and non-classical continuum theories. To illustrate the present doublet mechanics model, the influences of thickness to length scale parameter ratio of the considered material and slenderness ratio on static bending, buckling and vibration problems are investigated. It is shown that there are two frequency spectrums in the vibration of nanobeams similar to macro Timoshenko beams. It is interesting to note that acceptable physical frequencies (mode numbers) have an upper bound due to Van Hove singularity depending on geometrical and material properties of the beam. That fact is observed first time in the open literature by using scale dependent theories.
Noncoaxial vibration and buckling analysis of embedded double-walled carbon nanotubes by using doublet mechanics
(Elsevier Sci Ltd, 2018) Gul, Ufuk; Aydogdu, Metin
Free vibration and buckling of double-walled carbon nanotubes embedded in an elastic medium with simply supported boundary conditions are studied. Doublet Mechanics (DM) is used in the analysis. Macro level strains and stresses are defined in terms of micro level strains and stresses in the DM theory. These micro deformations and micro stresses are expanded in Taylor series and the number of terms in the Taylor series defines degree of the approach. Double-walled carbon nanotubes are modelled as Euler-Bernoulli beams embedded in an elastic medium. Critical buckling loads and free vibration frequencies are obtained by using DM and compared with the classical elasticity solutions. It is obtained that for some frequencies carbon nanotubes move noncoaxially. Noncoaxial vibration and buckling affect the physical properties of carbon nanotubes. The present results show that a length scale dependent DM can be used in the design of nano electro-mechanical systems.
Nonlinear wave modulation in nanorods using nonlocal elasticity theory
(Walter de Gruyter Gmbh, 2018) Gaygusuzoglu, Guler; Aydogdu, Metin; Gul, Ufuk
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 Schrodinger (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 cases.
On the Axial Vibration of Viscously Damped Short-Fiber-Reinforced Nano/Micro-composite Rods
(Springer Heidelberg, 2023) Gul, Ufuk; Aydogdu, Metin
Purpose The axial vibration of short fiber reinforced composite nanorods is investigated for the first time in this paper. Short fibers are randomly distributed or aligned in composite nanorods. Methods Nonlocal elasticity theory has been employed in the analysis. In addition to analytical solution of axial vibration problem of composite nanorods, finite element method is carried out to derive the natural frequencies for general boundary conditions. A two-noded rod finite element is used in the vibration problem. Results The natural frequencies of composite nanorods predicted by the present analytical model are verified with the developed finite element solution for general boundary conditions. In addition, the natural frequencies are obtained for the viscously damped case of composite nanorods. Conclusion The present study would be useful for the dynamic analyses of nanocomposite structures.
PLANE STRAIN POLAR ELASTICITY OF FIBRE-REINFORCED FUNCTIONALLY GRADED MATERIALS AND STRUCTURES
(Mathematical Science Publ, 2019) Soldatos, Konstantinos P.; Aydogdu, Metin; Gul, Ufuk
This study investigates the flexural response of a linearly elastic rectangular strip reinforced in a functionally graded manner by a single family of straight fibres resistant in bending. Fibre bending resistance is associated with the thickness of fibres which, in turn, is considered measurable through use of some intrinsic material length parameter involved in the definition of a corresponding elastic modulus. Solution of the relevant set of governing differential equations is achieved computationally, with the use of a well-established semianalytical mathematical method. A connection of this solution with its homogeneous fibre-reinforced material counterpart enables the corresponding homogeneous fibrous composite to be regarded as a source of a set of equivalent functionally graded structures, each one of which is formed through inhomogeneous redistribution of the same volume of fibres within the same matrix material. A subsequent stress and couple-stress analysis provides details of the manner in which the flexural response of the polar structural component of interest is affected by certain types of inhomogeneous fibre distribution.
SECOND SPECTRUM TIMOSHENKO BEAM VIBRATION ANALYSIS
(Int Inst Acoustics & Vibration, 2015) Gul, Ufuk; Aydogdu, Metin
In this study, vibration analysis of beams was studied using the classical Euler-Bernoulli and Timoshenko beam theories. Equations of motion and boundary conditions were obtained using the Hamilton's principle. Different boundary conditions were considered. Frequencies were obtained for both theories. Two dispersion curves were obtained in the wave propagation analysis using the Timoshenko beam theory whereas one curve was obtained for the Euler-Bernoulli beam theory. Frequencies obtained using different theories were compared and sec-ond spectrum of the Timoshenko beam theory was discussed in detail.
Structural modelling of nanorods and nanobeams using doublet mechanics theory
(Springer Heidelberg, 2018) Gul, Ufuk; Aydogdu, Metin
In this study, statics and dynamics of nanorods and nanobeams are investigated by using doublet mechanics. Classical rod theory and Euler-Bernoulli beam theory is used in the formulation. After deriving governing equations static deformation, buckling, vibration and wave propagation problems in nanorods and nanobeams are investigated in detail. The results obtained by using of doublet mechanics are compared to that of the classical elasticity theory. The importance of the size dependent mechanical behavior at the nano scale is shown in the considered problems. In doublet mechanics, bond length of atoms of the considered solid are used as an intrinsic length scale.
Transverse wave propagation analysis in single-walled and double-walled carbon nanotubes via higher-order doublet mechanics theory
(Taylor & Francis Ltd, 2021) Gul, Ufuk; Aydogdu, Metin
In the present study, transverse wave propagation in single-walled and double-walled carbon nanotubes is investigated based on doublet mechanics theory. The Euler-Bernoulli and Timoshenko beam theories are considered to study the wave dispersion relations of single-walled and double-walled carbon nanotubes (CNTs) with the set of relevant governing equations are achieved by use of the variational Hamilton's principle. Obtained governing equations are presented for zigzag and armchair CNT models. Using these models, scale dependent wave frequency, phase velocity and group velocity of CNTs are obtained. It has been observed that doublet mechanics results have so called van Hove singularity. This property is the first seen among the scale-dependent continuum theories. The effectiveness and validity of the present method are approved by comparing the predicted numerical results with molecular dynamics simulation and nonlocal Timoshenko beam theory. An excellent validation is obtained between the doublet mechanics based on Timoshenko beam theory and molecular dynamics simulation for phase velocities of (5,5) and (10,10) armchair single-walled CNTs. Also, this work clarifies the importance of the length scale effect on transverse wave dispersion in multi-walled CNTs.
Vibration analysis of Love nanorods using doublet mechanics theory
(Springer Heidelberg, 2019) Gul, Ufuk; Aydogdu, Metin
Longitudinal vibration of a nanorod is investigated based on the doublet mechanics theory with Love's assumption. By using Hamilton's principle, governing equation and corresponding boundary conditions are derived. Exact frequency equations are obtained for clamped-clamped and clamped-free boundary conditions. Obtained results are compared to the classical elasticity model, other size-dependent nonlocal theories and molecular dynamics simulation. The effects of the length scale parameter, rod length and lateral inertia are investigated.

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