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Öğe ANALYSIS OF FREE TORSIONAL VIBRATION IN CARBON NANOTUBES EMBEDDED IN A VISCOELASTIC MEDIUM(Lublin Univ Technology, Poland, 2015) Arda, Mustafa; Aydogdu, MetinCarbon 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.Öğe Axial dynamics of functionally graded Rayleigh-Bishop nanorods(Springer Heidelberg, 2021) Arda, MustafaPresent study considers the longitudinal dynamic analysis of carbon nanotubes which has been modeled as an axially functionally graded Rayleigh-Bishop rod with the help of nonlocal stress gradient elasticity theory. Governing equation of motion and boundary conditions for the axial dynamics of nanorod have been obtained with variational formulation. Ritz method has been used in the solution of the problem. Effects of lateral inertia and transverse deformation of carbon nanotubes, material composition properties and grading power-law index on the axial dynamics response have been investigated. Mode shapes of functionally graded Rayleigh-Bishop nanorod have been depicted in various cases. Boundary conditions and power-law index have important effect on dynamics of axially graded Rayleigh-Bishop nanorod. Present results could be useful at designing of nano-electromechanical devices.Öğe Çift eksenli ters sarkaç tasarımı ve kontrolü üzerine bir araştırma(Trakya Üniversitesi Fen Bilimleri Enstitüsü, 2012) Arda, Mustafa; Kuşçu, HilmiBu çalışmada iki eksenli ters sarkaç sisteminin Simulink'te modellenmesinin yapılması ve daha sonra fiziki ters sarkaç sistemi oluşturularak modelin test edilmesi amaçlanmıştır. İki eksenli ters sarkaç sistemi modellenirken iki ayrı alt sisteme ayrılmış, böylece problemin basitleştirilmesi hedeflenmiştir. Kontrol sistemi olarak PID (Proportional-Integral-Derivative) denetleyici kullanılmıştır. Çalışmada sadece sarkaç açısının kontrolü yapılarak sarkacın dik konumda kalması amaçlanmıştır. Sarkaç konumu kontrol edilmemektedir. Simülasyon sonuçları grafikler halinde gösterilerek hazırlanan modelin düzgün bir şekilde çalıştığı belirlenmiştir. Anahtar Kelimeler : Ters sarkaç, İki Boyutlu, PID Denetleyici, SimulinkÖğe Dynamic stability of harmonically excited nanobeams including axial inertia(Sage Publications Ltd, 2019) Arda, Mustafa; Aydogdu, MetinThis 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.Öğe Dynamics of nonlocal strain gradient nanobeams with longitudinal magnetic field(Wiley, 2021) Arda, Mustafa; Aydogdu, MetinFlexural dynamics of carbon nanotubes under the longitudinal magnetic field have been investigated in the paper. Carbon nanotube has been assumed as a hollow beam with circular cross section. Nonlocal strain gradient model has been employed in the modeling of nanobeam. Transverse component of Lorentz force, which occurs with longitudinal magnetic field, has been considered as an external force on nanobeam. Stress and strain energy functionals have been defined for the nonlocal strain gradient model using Hamilton principle. Higher-order governing differential equation of motion for the present problem has been solved with Differential Quadrature Method. Lorentz force and nonlocal strain gradient parameters have been considered in the standard and nonstandard boundary conditions in the present model formulation. Length scale and magnetic field parameters effect on the flexural vibration response of nanobeam have been investigated. Mode shapes of nonlocal strain gradient nanobeam have been depicted on various cases. Softening nonlocal strain gradient model gives physically consistent results and should be used in the analysis. Magnetic field effect shifts the mode shapes of clamped-free nanobeam. Present study could give useful results for designing of magnetically actuated nanomotors.Öğe Evaluation of optimum length scale parameters in longitudinal wave propagation on nonlocal strain gradient carbon nanotubes by lattice dynamics(Taylor & Francis Inc, 2022) Arda, MustafaLongitudinal wave propagation in carbon nanotubes has been investigated by using Rayleigh-Bishop rod model and nonlocal strain gradient elasticity theory in the present study. Size dependent governing equation of motion has been obtained with variational formulation. Validation of the proposed model has been achieved with developed lattice dynamics model which considers neighborhood interaction. Least squares approach has been used in addition to the traditional calibration methodology. Number of atomic interactions, shear strain and rotary inertia effects have important effects on the calibration of scale parameters. Present results could help to continuum modeling of carbon nanotubes with accurate scale parameters.Öğe Forced vibration of nanorods using nonlocal elasticity(Techno-Press, 2016) Aydogdu, Metin; Arda, MustafaPresent study interests with the longitudinal forced vibration of nanorods. The nonlocal elasticity theory of Eringen is used in modeling of nanorods. Uniform, linear and sinusoidal axial loads are considered. Dynamic displacements are obtained for nanorods with different geometrical properties, boundary conditions and nonlocal parameters. The nonlocal effect increases dynamic displacement and frequency when compared with local elasticity theory. Present results can be useful for modeling of the axial nanomotors and nanoelectromechanical systems.Öğe KISMİ YAYILI YÜK ETKİSİNDEKİ NANO KİRİŞLERİN DİNAMİK ANALİZİ(2020) Arda, MustafaKısmi yayılı yük etkisindeki karbon nanotüp kirişlerin dinamik analizigerçekleştirilmiştir. Nano kiriş için hareketin yönetici denklemi ve sınır şartlarıEringen’in Yerel Olmayan Elastisite Teorisi kullanılarak elde edilmiştir. Kısmi yayılıyük etkisi Heaviside fonksiyonu ile modellenmiştir. Oluşturulan model, nano kirişinparçalara bölünmesiyle elde edilen model sonuçlarıyla karşılaştırılarakdoğrulanmıştır. Nano kiriş titreşim frekansının yerel olmayan parametre, boyutsuzyayılı yük, yükün başlangıç noktası gibi parametrelerle değişimi incelenmiştir.Farklı titreşim frekanslarında çeşitli parametrelerin nano kirişin genlik değerlerineolan etkisi gösterilmiştir. Nano kirişin parçalara ayrılmasıyla artan süreklilik şartısayısının oluşturduğu yüksek boyutlu matrislerin çözümüne alternatif olarakoluşturulan modelde dört sınır şartıyla çözüme ulaşılmıştır. Bu çalışmanın sonuçlarıbakteri veya virüs gibi nano kütle sensörlerinin modellenmesinde kullanılabilir.Öğe Longitudinal magnetic field effect on torsional vibration of carbon nanotubes(Univ Tehran, 2018) Arda, Mustafa; Aydogdu, MetinTorsional 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 can be used in the design and analysis of nanoelectromechanical products like nano-motors.Öğe Longitudinal Vibration of Variable Cross-Sectional Nanorods(Trans Tech Publications Ltd, 2020) Arda, Mustafa; Aydogdu, MetinVibration 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.Öğe Nano ölçekli yapılarda burulma davranışının yerel olmayan elastisite teorisi kullanılarak statik ve dinamik analizi(Trakya Üniversitesi Fen Bilimleri Enstitüsü, 2016) Arda, Mustafa; Aydoğdu, MetinKarbon nanotüpler, sahip olduğu üstün fiziksel ve mekanik özelliklerinden dolayı birçok alanda kullanılabilme potansiyeline sahiptir. Karbon nanotüpler nano-motor, nano-yataklama elemanları, nano-dişli kutuları, nano-sensörler gibi nanoelektromekaniksel parçaların tasarmında kullanılabilirler. Nanotüplerin burulma davranışı geleceğin nano parçaları için önemli bir problem olabilir. Bu doktora çalışmasında, karbon nanotüplerin statik ve dinamik burulma analizi farklı durum çalışmalarında yapılmıştır. Nanotüp yapısı için sürekli ortam mekaniği modeli Eringen’in Yerel Olmayan Elastisite Teorisi’nden faydalanılarak oluşturulmuştur. Hareketin yönetici denklemleri ve sınır şartları Hamilton Prensibi’nden faydalanılarak çıkarılmıştır. Oluşturulan modelin geçerliliği Moleküler Dinamik Simülasyonu sonuçları ile karşılaştırılarak sağlanmıştır. Elastik ve viskoelastik ortamın, çok duvarlı yapılarda nanotüpler arasında oluşan van der Waals etkileşiminin ve basamak kesitli yapıların karbon nanotüp açısal yer değiştirmesine, burulma titreşimi ve dalga yayılımına olan etkisi araştırılmıştır.Yerel Olmayan Elastiste Teorisi karbon nanotüplerde klasik sürekli ortam mekaniğine göre daha gerçekçi sonuçlar vermektedir. Elde edilen sonuçların nanoelektromekaniksel parçaların üretimi ve tasarımında faydalı olacağı düşünülmektedir.Öğe Nonlocal Effect on Boundary Conditions of Cantilever Nanobeam(Amer Inst Physics, 2020) Arda, Mustafa; Aydogdu, MetinFree vibration of cantilever nanobeam has been investigated with the help of Eringen's Nonlocal Elasticity Theory. Nonlocal effect on boundary conditions have been taken into account. Variational energy formulation of nanobeam has been carried out for obtaining the nonlocal governing equation of motion and boundary conditions. Present model has been compared with the previous models. Enhancing phenomena in free vibration of cantilever nanobeams have been discussed with the help of nonlocal boundary condition effects.Öğe A Ritz Formulation for Vibration Analysis of Axially Functionally Graded Timoshenko-Ehrenfest Beams(Univ Tehran, Danishgah-I Tihran, 2022) Arda, Mustafa; Aydogdu, MetinDynamics of beams made of axially grading material has been analyzed in present work. Shear deformation and rotational inertia of the rectangular cross-sectional beam have been considered using Timoshenko-Ehrenfest beam model. Material properties of the beam have been assumed as a power-law function. Solution of the vibration problem of the axially functionally graded Timoshenko-Ehrenfest beam has been carried out with Ritz formulation. Present model has been validated with the previous literature works. Effects of power-law index parameter and grading material properties on the dynamics of axially functionally graded Timoshenko-Ehrenfest beam have been investigated. Transverse deflection and slope of the beam have been depicted in various cases. Present study can give useful results for designing of axially graded structural elements.Öğe Torsional dynamics of coaxial nanotubes with different lengths in viscoelastic medium(Springer Heidelberg, 2019) Arda, Mustafa; Aydogdu, MetinTorsional vibration analysis of double-walled carbon nanotube system embedded in viscoelastic medium is carried out in the present work. Hamilton's Principle is used for obtaining the governing equation and boundary conditions. van der Waals interaction between carbon nanotube walls is considered in circumferential direction. Characteristic frequency equations are obtained and solved for double-walled carbon nanotube system for various nonlocal parameters, viscoelastic medium parameters and van der Waals interactions. Results indicate that, viscoelastic medium yields the damping effect in vibration frequency parameter and the van der Waals interaction between nanotubes transmits this effect to the first nanotube with the help of nonlocality. The present results can be used in the design and analysis of biological nanomotors.Öğe Torsional statics and dynamics of nanotubes embedded in an elastic medium(Elsevier Sci Ltd, 2014) Arda, Mustafa; Aydogdu, MetinIn the present study, torsional statics and dynamics of Carbon Nanotubes (CNTs) embedded in elastic medium are studied using nonlocal elasticity theory. Governing equations of the CNT are obtained using the minimum energy principle. Effects of some parameters like stiffness of elastic medium, geometric properties of CNTs, nonlocal parameter and boundary conditions on the torsional statics and dynamics of CNTs are investigated in detail. Present results can be useful in design of future nano composites, nano electromechanical systems like nano position sensors and linear servomotors. (C) 2014 Elsevier Ltd. All rights reserved.Öğe Torsional Vibration Analysis of Carbon Nanotubes Using Maxwell and Kelvin-Voigt Type Viscoelastic Material Models(2020) Arda, MustafaTorsional dynamic analysis of viscoelastic Carbon Nanotubes (CNT) has been carried out in the presentwork. Maxwell and Kelvin-Voigt type viscoelasticity are considered in the modeling of viscoelastic material.Nonlocal Elasticity Theory is used in the formulation of governing equation of motion and boundary conditions.Viscoelasticity and nonlocal effects of structure on the free torsional vibration of CNTs have been investigated.Clamped-clamped and clamped-free boundary conditions are considered. Present study results could be usefulin design of nano-medicine delivery applications.Öğe Torsional vibration analysis of double walled carbon nanotubes using nonlocal elasticity(Springer Heidelberg, 2016) Aydogdu, Metin; Arda, MustafaIn the present study, the torsional vibration behavior of double walled carbon nanotubes (DWCNTs) is investigated using nonlocal elasticity theory. The effects of van der Waals Force interaction, nanotube length and nonlocal parameter are studied in detail. Two frequency set are obtained for DWCNTs for a given half wave number. It is also shown that some mode shapes are anti-phase and some of them are in-phase. The present results can be useful in design of nano electromechanical systems like nanobearings and rotary servomotors.Öğe Torsional wave propagation in multiwalled carbon nanotubes using nonlocal elasticity(Springer Heidelberg, 2016) Arda, Mustafa; Aydogdu, MetinTorsional wave propagation in multiwalled carbon nanotubes is studied in the present work. Governing equation of motion of multiwalled carbon nanotube is obtained using Eringen's nonlocal elasticity theory. The effect of van der Waals interaction coefficient is considered between inner and outer nanotubes. Dispersion relations are obtained and discussed in detail. Effect of nonlocal parameter and van der Waals interaction to the torsional wave propagation behavior of multiwalled carbon nanotubes is investigated. It is obtained that torsional van der Waals interaction between adjacent tubes can change the rotational direction of multiwalled carbon nanotube as inphase or anti-phase. The group and escape velocity of the waves converge to a limit value in the nonlocal elasticity approach.Öğe TORSIONAL WAVE PROPAGATION OF CNTS VIA DIFFERENT NONLOCAL GRADIENT THEORIES(Int Inst Acoustics & Vibration, 2016) Arda, Mustafa; Aydogdu, MetinCarbon nanotubes (CNTs) have great potential in many areas due to the advantage of their superior mechanical and physical properties. CNTs can be used in designing of nano-electromechanical products (nano-motors, nano-bearings, nano-gearboxes etc.), nano-transistors (in CPU), nano-pharmaceutical products, nano-sensors, etc... In static and dynamic analysis of CNTs, continuum models are more applicable. Because of the size independence, classical theories could not be applied in nanoscale. The Nonlocal Theory, a continuum model includes size dependency, can be applied as stress, strain and combined gradient forms. In the present study, torsional wave propagation of CNTs was investigated according to nonlocal stress, strain and combined gradient theories. Effects of the small scale parameters to the wave frequency were obtained. Results were compared with the Molecular Dynamics Simulations and Lattice Dynamics. Nonlocal strain gradient approach shows more weakening effect on CNT rather than the nonlocal stress gradient approach.Öğe Vibration analysis of carbon nanotube mass sensors considering both inertia and stiffness of the detected mass(Taylor & Francis Inc, 2022) Arda, Mustafa; Aydogdu, MetinDynamic response of a carbon nanotube mass sensor has been analyzed in the present study. In addition to the previous works, the detected mass has been assumed as an elastic body which has its own stiffness. Euler-Bernoulli beam model has been used in obtaining equation of motion of the nanobeam mass sensor with Hamilton principle and nonlocal elasticity theory. Ritz method has been used in the solution. Proposed model has been validated with comparing present and previous results of macro scale mass-sensor studies. The effect of mass and stiffness ratio, position of the detected mass and nonlocal parameter on the vibration frequency of nanobeam mass sensor has been investigated. It is obtained that consideration of the stiffness of the detected mass adds a new frequency to the spectrum of the nanobeam and shifts the nanobeam's frequencies to the one higher adjacent mode. Present results could be useful at design of biological tissue or virus sensors. Communicated by Krzysztof Kamil Zur.
