Nonlinear vibration and stability analysis of a size-dependent viscoelastic cantilever nanobeam with axial excitation

Noroozi, Mohammad; Ghadiri, Majid

doi:10.1177/0954406220959104

Cited by 5 publications

(4 citation statements)

References 55 publications

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“…After that, plenty of researches are accomplished to analyse the bending, buckling, and vibration response of distinct nano-structures such as nano sized beams, plates, and shells using this theory. [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33] Researchers have also used the nonlocal theory to study the cracks in the macro-structures. 34 Recently, Van et al 35 presented a size-dependent refined plate theory and studied the bending and vibrations of graphenereinforced composite nano-plates with different types of gradation of graphene platelets.…”

Section: Introductionmentioning

confidence: 99%

Stochastic thermo-elastic vibration characteristics of functionally graded porous nano-beams using first-order perturbation-based nonlocal finite element model

Chandel

Talha

2022

Proceedings of the Institution of Mechanical Engineers, Part C:

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This paper emphasized the size-dependent thermo-elastic vibration characteristics of uncertain functionally graded (FG) porous nano-beams by employing the first-order perturbation theory (FOPT) with the finite element method. An isoparametric quadratic beam element having three nodes is used for the finite element analysis of the nano-beams with variation in degree of uncertainty in material properties, geometric configuration, and thermal environment. The power-law model is employed to obtain the effective material properties of the considered beams. The governing equations are presented according to Eringen’s elasticity theory and Reddy’s beam theory using the minimum potential energy. The computed FOPT results for the vibration statistics are assessed with the help of Monte Carlo simulation (MCS) and a well agreement is found. Further, results are presented by analyzing the effects of degree of source uncertainty, size-dependent parameter, volume fraction indices, porosity distribution, porosity index, thermal environment, and aspect ratios on the fundamental frequency of the FGM nano-beams. The numerical results revealed the significant influence of thermal environment and porosity on the vibration statistics of the nano-beams and provided guidance for the precise and reliable design of nano-devices for the application in thermal environment.

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Section: Introductionmentioning

confidence: 99%

Stochastic thermo-elastic vibration characteristics of functionally graded porous nano-beams using first-order perturbation-based nonlocal finite element model

Chandel

Talha

2022

Proceedings of the Institution of Mechanical Engineers, Part C:

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“…Micro-/nano-sensors are one of the representative elements of micro-/nanoelectromechanical systems (MEMS/NEMS) that found a variety of applications in pioneering engineering systems [1,2]. Structural analysis of vibrating modules of MEMS/NEMS is a challenging issue that stimulated a great deal of interest [3][4][5][6][7][8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Dynamic Characteristics of Mixture Unified Gradient Elastic Nanobeams

Faghidian

Tounsi

2022

FU Mech Eng

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The mixture unified gradient theory of elasticity is invoked for the rigorous analysis of the dynamic characteristics of elastic nanobeams. A consistent variational framework is established and the boundary-value problem of dynamic equilibrium enriched with proper form of the extra non-standard boundary conditions is detected. As a well-established privilege of the stationary variational theorems, the constitutive laws of the resultant fields cast as differential relations. The wave dispersion response of elastic nano-sized beams is analytically addressed and the closed form solution of the phase velocity is determined. The free vibrations of the mixture unified gradient elastic beam is, furthermore, analytically studied. The dynamic characteristics of elastic nanobeams is numerically evaluated, graphically illustrated, and commented upon. The efficacy of the established augmented elasticity theory in realizing the softening and stiffening responses of nano-sized beams is evinced. New numerical benchmark is detected for dynamic analysis of elastic nanobeams. The established mixture unified gradient elasticity model provides a practical approach to tackle dynamics of nano-structures in pioneering MEMS/NEMS.

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“…They pointed out that the differential form of the ENET may get paradoxical results when dealing with the cantilever boundary condition. Noroozi and Ghadiri 57 presented the nonlinear forced vibration and stability analysis of axially movable cantilevered nanobeams subjected to a harmonic external excitation with consideration of linear damping.…”

Section: Introductionmentioning

confidence: 99%

Size-dependent vibration of functionally graded rotating nanobeams with different boundary conditions based on nonlocal elasticity theory

Fang

Yin

Zhang

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part C:

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The free vibration of rotating functionally graded nanobeams under different boundary conditions is studied based on nonlocal elasticity theory within the framework of Euler-Bernoulli and Timoshenko beam theories. The thickness-wise material gradient variation of the nanobeam is considered. By introducing a second-order axial shortening term into the displacement field, the governing equations of motion of the present new nonlocal model of rotating nanobeams are derived by the Hamilton’s principle. The nonlocal differential equations are solved through the Galerkin method. The present nonlocal models are validated through the convergence and comparison studies. Numerical results are presented to investigate the influences of the nonlocal parameter, angular velocity, material gradient variation together with slenderness ratio on the vibration of rotating FG nanobeams with different boundary conditions. Totally different from stationary nanobeams, the rotating nanobeams with relatively high angular velocity could produce larger fundamental frequencies than local counterparts. Additionally, the axial stretching-transverse bending coupled vibration is perfectly shown through the frequency loci veering and modal conversion.

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Nonlinear vibration and stability analysis of a size-dependent viscoelastic cantilever nanobeam with axial excitation

Cited by 5 publications

References 55 publications

Stochastic thermo-elastic vibration characteristics of functionally graded porous nano-beams using first-order perturbation-based nonlocal finite element model

Stochastic thermo-elastic vibration characteristics of functionally graded porous nano-beams using first-order perturbation-based nonlocal finite element model

Dynamic Characteristics of Mixture Unified Gradient Elastic Nanobeams

Size-dependent vibration of functionally graded rotating nanobeams with different boundary conditions based on nonlocal elasticity theory

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