Free and forced vibration nonlinear analysis of a microbeam using finite strain and velocity gradients theory

Fernandes, Ralston; Mousavi, Seyed Mahmoud; El-Borgi, Sami

doi:10.1007/s00707-016-1646-x

Cited by 23 publications

(2 citation statements)

References 37 publications

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“…Fernandes et al [40] considered the nonlinear vibration problem of a carbon nanotube bar embedded in an elastic medium using the strain and velocity gradient theory. In another study, Fernandes et al [41] examined the nonlinear free and forced vibration response of a microbeam using finite strain and velocity gradient theory. Finally, El-Borgi et al [42] studied the torsional vibration of viscoelastic rods using nonlocal strain and velocity gradient theory.…”

Section: Accepted Manuscriptmentioning

confidence: 99%

Static and dynamic response of CNT nanobeam using nonlocal strain and velocity gradient theory

Ouakad

El-Borgi²,

Mousavi³

et al. 2018

Applied Mathematical Modelling

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This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Highlights • We study length-scale effect on response of an actuated CNT nano-actuator using a nonlocal strain-Velocity gradient theory. • The nano-actuator is modeled as a Euler-Bernoulli beam which accounts for von-Karman strain and electric actuating forcing. • Three length-scale parameters are included, namely a nonlocal, a strain gradient, and a velocity gradient parameter. • Equation of motion and boundary conditions are derived using Hamilton's principle and DQM was used to discretize the problem. • The main objective is to study the effect of length-scale parameters on nonlinear vibrational response of the nano-actuator.

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Section: Accepted Manuscriptmentioning

confidence: 99%

Static and dynamic response of CNT nanobeam using nonlocal strain and velocity gradient theory

Ouakad

El-Borgi²,

Mousavi³

et al. 2018

Applied Mathematical Modelling

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“…Vibration analysis of micro-structures has attracted a lot of researchers in the last decade. Plenty of papers has been published on mircobeams [8][9][10][11][12][13], microbars [14,15] and micro plates [16,17] taking the length-scale parameters into account.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Vibration Analysis of Axially Functionally Graded Microbeams Based on Nonlinear Elastic Foundation Using Modified Couple Stress Theory

Alimoradzadeh

Salehi

Esfarjani

2020

Period. Polytech. Mech. Eng.

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In this study, a non-classical approach was developed to analyze nonlinear free and forced vibration of an Axially Functionally Graded (AFG) microbeam by means of modified couple stress theory. The beam is considered as Euler-Bernoulli type supported on a three-layered elastic foundation with Von-Karman geometric nonlinearity. Small size effects included in the analysis by considering the length scale parameter. It is assumed that the mass density and elasticity modulus varies continuously in the axial direction according to the power law form. Hamilton's principle was implemented to derive the nonlinear governing partial differential equation concerning associated boundary conditions. The nonlinear partial differential equation was reduced to some nonlinear ordinary differential equations via Galerkin's discretization technique. He's Variational iteration methods were implemented to obtain approximate analytical expressions for the frequency response as well as the forced vibration response of the microbeam with doubly-clamped end conditions. In this study, some factors influencing the forced vibration response were investigated. Specifically, the influence of the length scale parameter, the length of the microbeam, the power index, the Winkler parameter, the Pasternak parameter, and the nonlinear parameter on the nonlinear natural frequency as well as the amplitude of forced response have been investigated.

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Size effects on centrosymmetric anisotropic shear deformable beam structures

Yaghoubi

Mousavi

Paavola

2016

Z. Angew. Math. Mech.

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In this paper, the size effect on beam structures with centrosymmetric anisotropy is studied within strain gradient elasticity theory. Applying dimension reduction to the three dimensional anisotropic gradient elasticity, the third-order shear deformable (TSD) beam is analysed. A variational approach is used to determine the equilibrium equations of TSD beam together with consistent (classical and non-classical) boundary conditions. The TSD beam theory which is suitable for deep beam structures can be replaced by (less complicated) Euler-Bernoulli beam model for thin beam structures. The anisotropic Euler-Bernoulli beam model is also formulated within the framework of strain gradient theory. This anisotropic beam theory can be used to study size effects for any types of centrosymmetric anisotropy. To address the more practical cases of composite structures, the formulation is simplified for orthotropic and transversely isotropic materials. Finally, the analytical solutions are provided for bending of simply supported (TSD and Euler-Bernoulli) beams as well as clamped Euler-Bernoulli beams. The effect of the crystal orientation with respect to the beam geometry is investigated in these examples.

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Free and forced vibration nonlinear analysis of a microbeam using finite strain and velocity gradients theory

Cited by 23 publications

References 37 publications

Static and dynamic response of CNT nanobeam using nonlocal strain and velocity gradient theory

Static and dynamic response of CNT nanobeam using nonlocal strain and velocity gradient theory

Nonlinear Vibration Analysis of Axially Functionally Graded Microbeams Based on Nonlinear Elastic Foundation Using Modified Couple Stress Theory

Size effects on centrosymmetric anisotropic shear deformable beam structures

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