Vibration analysis of a single-walled carbon nanotube under action of a moving harmonic load based on nonlocal elasticity theory

Şi̇mşek, Mesut

doi:10.1016/j.physe.2010.07.003

Cited by 195 publications

(32 citation statements)

References 64 publications

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“…Simsek [35] investigated the influence of a moving load on different types of single-walled carbon nanotubes. Karaoglu and Aydogdu [36] investigated the forced vibration of carbon nanotubes via nonlocal EulerBernoulli beam model.…”

Section: Introductionmentioning

confidence: 99%

Dynamic stability of a nonlinear multiple-nanobeam system

2018

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We use the incremental harmonic balance (IHB) method to analyse the dynamic stability problem of a nonlinear multiple-nanobeam system (MNBS) within the framework of Eringen's nonlocal elasticity theory. The nonlinear dynamic system under consideration includes MNBS embedded in a viscoelastic medium as clamped chain system, where every nanobeam in the system is subjected to time-dependent axial loads. By assuming the von Karman type of geometric nonlinearity, a system of m nonlinear partial differential equations of motion is derived based on the Euler-Bernoulli beam theory and D' Alembert's principle. All nanobeams in MNBS are considered with simply supported boundary conditions. Semi-analytical solutions for time response functions of the nonlinear MNBS are obtained by using the single-mode Galerkin discretization and IHB method, which are then validated by using the numerical integration method. Moreover, Floquet theory is employed to determine the sta- method, we obtain an incremental relationship with the frequency and amplitude of time-varying axial load, which defines stability boundaries. Numerical examples show the effects of different physical and material parameters such as the nonlocal parameter, stiffness of viscoelastic medium and number of nanobeams on Floquet multipliers, instability regions and nonlinear amplitude-frequency response curves of MNBS. The presented results can be useful as a first step in the study and design of complex micro/nanoelectromechanical systems.

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Section: Introductionmentioning

confidence: 99%

Dynamic stability of a nonlinear multiple-nanobeam system

2018

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“…In the nonlocal elasticity theory proposed by Eringen [1], to account for scale effect it is assumed that the stress at a point is a function of strains at all points in the continuum. A large number of studies related with static [5,6], buckling [7][8][9][10][11][12] and vibration [13][14][15][16][17][18][19][20] analysis of nanostructures using Eringen's nonlocal elasticity theory can be found in literature.…”

Section: Introductionmentioning

confidence: 99%

Yerel Olmayan Şekil Değiştirme Gradyanı Teorisi Kullanılarak Elastik Zemine Gömülü Nano Çubuğun Eksenel Titreşim Analizi

Şi̇mşek¹

2016

Çukurova Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi

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Size-dependent axial vibration of a nanorod embedded in elastic medium is studied for the first time in this paper within the framework of the nonlocal strain gradient theory. The governing equation of motion of the problem is derived using the equilibrium condition and it is solved analytically to obtain the exact expression of vibration frequency for a fixed-fixed nanorod. The influences of the nonlocal parameter, the material length scale parameter and the elastic medium coefficient on the free vibration frequencies are investigated in detail. The results show that free vibration frequencies are significantly dependent on the size effects, and the size effects gain more importance at higher modes. Therefore, the classical continuum theory is inappropriate to investigate the mechanical behavior of nanostructures.Keywords: Nanotechnology, Vibration, Nonlocal elasticity theory, Strain gradient theory, Nanorod Yerel Olmayan Şekil Değiştirme Gradyanı Teorisi Kullanılarak Elastik Zemine Gömülü Nano Çubuğun Eksenel Titreşim Analizi ÖzetElastik zemine gömülü bir nano çubuğun boyut etkisine bağlı eksenel titreşimi yerel olmayan şekil değiştirme gradyanı teorisi çerçevesinde ilk olarak bu çalışmada incelenmiştir. Probleme ait yönetici hareket denklemi denge şartı kullanılarak çıkarılmış, iki ucu ankastre nano çubuğun serbest titreşim frekansına ait kesin ifadeyi elde etmek için yönetici denklem analitik olarak çözülmüştür. Yerel olmayan parametre, malzeme uzunluk ölçek parametresi ve elastik zemin parametresinin serbest titreşim frekansları üzerindeki etkisi detaylı olarak incelenmiştir. Elde edilen sayısal sonuçlar göstermiştir ki; serbest titreşim frekansları boyut etkisine önemli derecede bağlıdır ve boyut etkisi yüksek modlarda daha çok önem kazanmaktadır. Bu nedenlerden dolayı, klasik sürekli ortamlar mekaniği nano ölçekteki yapıların analizi için uygun değildir.

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“…A nonlocal Euler-Bernoulli beam model was established to obtain frequency equation and model shape functions of simply supported, clamped and cantilever beams [37]. Forced vibration of a simply supported SWCNT subjected to a moving harmonic load was investigated by using nonlocal Euler-Bernoulli beam theory [38]. The vibration characteristics of SWCNTs with different boundary conditions subjected to initial strain was studied in [39].…”

Section: Introductionmentioning

confidence: 99%

Non-linear vibration of nanobeams with various boundary condition based on nonlocal elasticity theory

Bağdatlı

2015

Composites Part B: Engineering

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Vibration analysis of a single-walled carbon nanotube under action of a moving harmonic load based on nonlocal elasticity theory

Cited by 195 publications

References 64 publications

Dynamic stability of a nonlinear multiple-nanobeam system

Dynamic stability of a nonlinear multiple-nanobeam system

Yerel Olmayan Şekil Değiştirme Gradyanı Teorisi Kullanılarak Elastik Zemine Gömülü Nano Çubuğun Eksenel Titreşim Analizi

Non-linear vibration of nanobeams with various boundary condition based on nonlocal elasticity theory

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