Complex modal analysis of transverse free vibrations for axially moving nanobeams based on the nonlocal strain gradient theory

Wang, Jing; Shen, Huoming; Zhang, Bo; Liu, Juan; Zhang, Yingrong

doi:10.1016/j.physe.2018.03.017

Cited by 51 publications

(30 citation statements)

References 44 publications

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“…They concluded that the natural frequency of the system first decreases slightly, and then increases rapidly with an increase in the system velocity. Wang et al [17] utilized complex modal analysis to evaluate the role of modal truncation order on the transverse free vibration response of axially moving nanobeams by considering von Karman geometric nonlinearity. They declared that the natural frequencies of the nanobeam have a significant dependency on the size effect of the mechanical properties of the system.…”

Section: Introductionmentioning

confidence: 99%

On the Vibrations and Stability of Moving Viscoelastic Axially Functionally Graded Nanobeams

et al. 2020

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In this article, size-dependent vibrations and the stability of moving viscoelastic axially functionally graded (AFG) nanobeams were investigated numerically and analytically, aiming at the stability enhancement of translating nanosystems. Additionally, a parametric investigation is presented to elucidate the influence of various key factors such as axial gradation of the material, viscosity coefficient, and nonlocal parameter on the stability boundaries of the system. Material characteristics of the system vary smoothly along the axial direction based on a power-law distribution function. Laplace transformation in conjunction with the Galerkin discretization scheme was implemented to obtain the natural frequencies, dynamical configuration, divergence, and flutter instability thresholds of the system. Furthermore, the critical velocity of the system was evaluated analytically. Stability maps of the system were examined, and it can be concluded that the nonlocal effect in the system can be significantly dampened by fine-tuning of axial material distribution. It was demonstrated that AFG materials can profoundly enhance the stability and dynamical response of axially moving nanosystems in comparison to homogeneous materials. The results indicate that for low and high values of the nonlocal parameter, the power index plays an opposite role in the dynamical behavior of the system. Meanwhile, it was shown that the qualitative stability of axially moving nanobeams depends on the effect of viscoelastic properties in the system, while axial grading of material has a significant role in determining the critical velocity and natural frequencies of the system.

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Section: Introductionmentioning

confidence: 99%

On the Vibrations and Stability of Moving Viscoelastic Axially Functionally Graded Nanobeams

et al. 2020

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“…where where the maximum limitations related to the values of Young's modulus and mass density of the FGPM in order are denoted by Ẽ and ̃. By taking the Gaussian Random Field model [29] into consideration, the associated mass density coefficient ( m ) is defined in terms of the porosity coefficient ( p ) as below Also, with the aid of the closed-cell Gaussian Random Field model [74], the value of the Poisson's ratio for a FGPM is estimated as It should be noted that in order to remain the mass density of the FGPM as a constant value, the correct value of s 0 is extracted as…”

Section: Surface Elastic Fgpm Shell Modelmentioning

confidence: 99%

“…(18) and (28) into Eqs. (24c) and (29), the non-classical differential equations related to the nonlinear oscillations of a FGPM nanoshell in the presence of the surface stress are obtained as in which…”

Section: Surface Elastic Fgpm Shell Modelmentioning

confidence: 99%

“…Sahmani and Aghdam [27,28] examined the nonlinear postbuckling behavior of supramolecular protein micro/nanotubules based on the nonlocal strain gradient theory. Wang et al [29] conducted a complex modal analysis of an axially moving nonlocal strain gradient nanobeam. Hajmohammad et al [30] explored the bending and buckling responses of FG annular microplates coated with piezoelectric layers.…”

Section: Introductionmentioning

confidence: 99%

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On size-dependent large-amplitude free oscillations of FGPM nanoshells incorporating vibrational mode interactions

Sahmani

Safaei

2020

Archiv.Civ.Mech.Eng

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At nanoscale, surface free energies of the atoms located on the free surfaces of structures significantly affect their mechanical characteristics. In this study, nonlinear large-amplitude free vibration response of nanoshells prepared from functionally graded porous materials (FGPM) is investigated by taking into account surface stress size effects and vibrational mode interactions. Non-classical shell model is constructed on the basis of the Gurtin-Murdoch type of the surface theory of elasticity having the capability of capturing surface stress size dependency. The accuracy of nonlinear vibration analysis is improved by incorporating the interaction of the main vibration mode and the first, third and fifth symmetric oscillation modes. Moreover, the closed-cell Gaussian-Random field scheme is put to use to extract the mechanical characteristics of FGPM nanoshell. Multiple timescales technique is then applied to achieve surface stress elastic-based nonlinear frequency of FGPM nanoshell analytically for different interactions between vibrational modes. It is revealed that by incorporating the interactions of the main vibration mode and higher symmetric oscillation modes, the behavior of the backbone curves belongs to the nonlinear free oscillation response of FGPM nanoshells changes from hardening to softening schema. It is found that when only the main vibration mode is taken into account, surface elasticity effects makes an enhancement in the significance of the hardening schema. However, by considering the interactions of higher symmetric oscillation modes, surface elasticity effects makes a reduction in the significance of the softening schema.

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“…In addition, size influences have been studied on the nonlinear mechanics of microscale structures in recent years [31][32][33]. 4 Recently, it has been reported that taking into account both the stress nonlocality and strain gradients leads to a more reliable size-dependent theoretical model for nanorods [34], nanobeams [35][36][37], functionally graded nanostructures [38,39], protein microtubules [40] and graphene sheets [41]. However, all of the above-described valuable theoretical models of size-dependent imperfect nanoscale structures contain only one scale parameter (mainly only one nonlocal parameter) which is incapable of incorporating the size effect thoroughly.…”

Section: Introductionmentioning

confidence: 99%

Large-amplitude coupled scale-dependent behaviour of geometrically imperfect NSGT nanotubes

Farajpour

Ghayesh

Farokhi

2019

International Journal of Mechanical Sciences

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In this paper, a scale-dependent coupled nonlinear continuum-based model is developed for the mechanical behaviour of imperfect nanoscale tubes incorporating both the effect of the stress nonlocality and strain gradient effects. The scale effects on the nonlinear mechanics are taken into consideration employing a modified elasticity theory on the basis of a refined combination of Eringen's elasticity and the strain gradient theory. According to the Euler-Bernoulli theory of beams, the nonlocal strain gradient theory (NSGT) and Hamilton's principle, the potential energy, kinetic energy and the work performed by harmonic loads are formulated, and then the coupled scale-dependent equations of the imperfect nanotube are derived. Finally, Galerkin's scheme, as a discretisation technique, and the continuation method, as a solution procedure for ordinary differential equations, are used. The effects of geometrical imperfections in conjunction with other nanosystem parameters such as the nonlocal coefficient as well as the strain gradient coefficient on the coupled large-amplitude mechanical behaviour are explored and discussed.

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Complex modal analysis of transverse free vibrations for axially moving nanobeams based on the nonlocal strain gradient theory

Cited by 51 publications

References 44 publications

On the Vibrations and Stability of Moving Viscoelastic Axially Functionally Graded Nanobeams

On the Vibrations and Stability of Moving Viscoelastic Axially Functionally Graded Nanobeams

On size-dependent large-amplitude free oscillations of FGPM nanoshells incorporating vibrational mode interactions

Large-amplitude coupled scale-dependent behaviour of geometrically imperfect NSGT nanotubes

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