Damped forced vibration analysis of single-walled carbon nanotubes resting on viscoelastic foundation in thermal environment using nonlocal strain gradient theory

Malikan, Mohammad; Nguyen, Van Bac; Tornabene, Francesco

doi:10.1016/j.jestch.2018.06.001

Cited by 46 publications

(24 citation statements)

References 52 publications

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“…Moreover, e shows a physical constant and a=0.142 nm is the bond length of carbon-carbon atoms. By substituting equation (12) into equations (7a), (7b), the small-scale stress resultants can be obtained as [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48]…”

Section: The Size-dependent Effectsmentioning

confidence: 99%

Post-critical buckling of truncated conical carbon nanotubes considering surface effects embedding in a nonlinear Winkler substrate using the Rayleigh-Ritz method

Malikan

Eremeyev

2020

Mater. Res. Express

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This research predicts theoretically post-critical axial buckling behavior of truncated conical carbon nanotubes (CCNTs) with several boundary conditions by assuming a nonlinear Winkler matrix. The post-buckling of CCNTs has been studied based on the Euler-Bernoulli beam model, Hamilton's principle, Lagrangian strains, and nonlocal strain gradient theory. Both stiffness-hardening and stiffness-softening properties of the nanostructure are considered by exerting the second stressgradient and second strain-gradient in the stress and strain fields. Besides small-scale influences, the surface effect is also taken into consideration. The effect of the Winkler foundation is nonlinearly taken into account based on the Taylor expansion. A new admissible function is used in the Rayleigh-Ritz solution technique applicable for buckling and post-buckling of nanotubes and nanobeams. Numerical results and related discussions are compared and reported with those obtained by the literature. The significant results proved that the surface effect and the nonlinear term of the substrate affect the CCNT considerably.

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Section: The Size-dependent Effectsmentioning

confidence: 99%

Post-critical buckling of truncated conical carbon nanotubes considering surface effects embedding in a nonlinear Winkler substrate using the Rayleigh-Ritz method

Malikan

Eremeyev

2020

Mater. Res. Express

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“…The dynamic equilibrium of the model is derived with the calculus of variations on the basis of the Hamilton's principle leading to formulating governing equations [48]  …”

Section: Theoretical Modellingmentioning

confidence: 99%

“…Afterwards, the outcomes for variety of cases would be depicted numerically. Regarding the refined shear deformation beam theory [48], the given displacement field is described as…”

Section: Introduction and Literature Reviewmentioning

confidence: 99%

Vibro-Electrical Behavior of a Viscoelastic Piezo-Nanowire in an Elastic Substrate Considering Stress Nonlocality and Microstructural Size-Dependent Effects

Malikan

2019

International Journal of Engineering and Applied Sciences

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This research deals with dynamic response of a Polymer/BaTiO3 nanowire including viscosity influences. The wire is also impressed by a longitudinal electric field. Hamilton's principle, Lagrangian strains and a refined higher-order beam theory are combined together in order to derive equations of motion. By combining nonlocality and small size effects of a unique model into the derived equations, the couple relations which describe nanosize behavior in a small scale are presented. By employing an analytical approach, the fundamental natural frequencies are calculated numerically. The important results display that the effect of internal viscosity and nonlocality whenever the nanowire is very large are pointless.

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“…In the vibrational context, temperature has a significant influence on the frequency shift [13]. Thus, a good part of research efforts on nonlocal beams in nonisothermal environments are devoted to dynamical analysis [14]. Composite beams in this context are analysed in [15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Nonlocal integral thermoelasticity: A thermodynamic framework for functionally graded beams

Barretta

Čanađija

Sciarra

2019

Composite Structures

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An effective nonlocal integral formulation for functionally graded Bernoulli-Euler beams in nonisothermal environment is developed. Both thermal and mechanical loadings are accounted for. The proposed model, of stress-driven integral type, is shown to be governed by a thermodynamically consistent differential problem with proper constitutive boundary conditions. The new thermoelastic strategy is illustrated by investigating a set of examples. It is demonstrated that in nonisothermal statically indeterminate problems rather complex structural behaviours can appear and that both the shift of the neutral surface and nonlocality have a dominating influence at small-scales.

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Damped forced vibration analysis of single-walled carbon nanotubes resting on viscoelastic foundation in thermal environment using nonlocal strain gradient theory

Cited by 46 publications

References 52 publications

Post-critical buckling of truncated conical carbon nanotubes considering surface effects embedding in a nonlinear Winkler substrate using the Rayleigh-Ritz method

Post-critical buckling of truncated conical carbon nanotubes considering surface effects embedding in a nonlinear Winkler substrate using the Rayleigh-Ritz method

Vibro-Electrical Behavior of a Viscoelastic Piezo-Nanowire in an Elastic Substrate Considering Stress Nonlocality and Microstructural Size-Dependent Effects

Nonlocal integral thermoelasticity: A thermodynamic framework for functionally graded beams

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