Studying linear and nonlinear vibrations of fractional viscoelastic Timoshenko micro-/nano-beams using the strain gradient theory

Ansari, R.; Oskouie, M. Faraji; Rouhi, H.

doi:10.1007/s11071-016-3069-6

Cited by 36 publications

(12 citation statements)

References 45 publications

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“…Ansari et. al [22] studied the nonlinear vibration analysis of the micro/nano beams using strain gradient theory. Farokhi and Ghayesh [23] studied the viscoelasticity effects on resonant response of a shear deformable extensible microbeam.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear vibration analysis of the nanobeams subjected to magneto-electro-thermo loading based on a novel HSDT

Mohammadi¹

2021

Preprint

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In this paper, the nonlinear vibration analysis of the nanobeams subjected to magneto-electro-thermo loading based on a novel HSDT is studied. Nonlocal elasticity theory is applied to consider the small scale effect. The nonlinear equations of motion are derived using Hamilton’s principle. First, a Galerkin-based numerical technique is applied to reduce the nonlinear governing equation into a set of Duffing-type time-dependent differential equations. Afterward, the analytical solutions are derived based on the method of multiple scales (MMS) and perturbation technique. All of the mechanical properties of the beam are temperature dependent. The impacts of the several variables are investigated on the nonlinear frequency ratio of the nanobeams. The results illustrate that when maximum deflection is smaller/ greater than 0.2, its impact on the nonlinear frequency ratio will decrease/increase.

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Section: Introductionmentioning

confidence: 99%

Nonlinear vibration analysis of the nanobeams subjected to magneto-electro-thermo loading based on a novel HSDT

Mohammadi¹

2021

Preprint

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“…The successful application of fractional calculus to the problems of viscoelastic nanostructures has been recently reported in previous studies. 40–45 In the current work, in the contexts of fractional calculus and nonlocal theory, the vibrations of viscoelastic CNTs conveying fluid and resting on the viscoelastic Winkler foundation are studied. To derive the basic relations, the nonlocal version of Timoshenko beam theory, KV viscoelastic model, and Hamilton’s principle are applied.…”

Section: Introductionmentioning

confidence: 99%

Investigating vibrations of viscoelastic fluid-conveying carbon nanotubes resting on viscoelastic foundation using a nonlocal fractional Timoshenko beam model

Oskouie

Ansari

Rouhi

2020

Proceedings of the Institution of Mechanical Engineers, Part N:

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On the basis of fractional viscoelasticity, the size-dependent free-vibration response of viscoelastic carbon nanotubes conveying fluid and resting on viscoelastic foundation is studied in this article. To this end, a nonlocal Timoshenko beam model is developed in the context of fractional calculus. Hamilton’s principle is applied in order to obtain the fractional governing equations including nanoscale effects. The Kelvin–Voigt viscoelastic model is also used for the constitutive equations. The free-vibration problem is solved using two methods. In the first method, which is limited to the simply supported boundary conditions, the Galerkin technique is employed for discretizing the spatial variables and reducing the governing equations to a set of ordinary differential equations on the time domain. Then, the Duffing-type time-dependent equations including fractional derivatives are solved via fractional integrator transfer functions. In the second method, which can be utilized for carbon nanotubes with different types of boundary conditions, the generalized differential quadrature technique is used for discretizing the governing equations on spatial grids, whereas the finite difference technique is used on the time domain. In the results, the influences of nonlocality, geometrical parameters, fractional derivative orders, viscoelastic foundation, and fluid flow velocity on the time responses of carbon nanotubes are analyzed.

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“…Subsequently, using Mindlin's formulation, the strain gradient theory was proposed by Fleck and Hutchinson [8{10] ,which considers only the rst derivatives of the strain tensor. Ansari [11] developed a model using the modi ed strain gradient theory to describe the linear and nonlinear vibrational behavior of fractional viscoelastic Timoshenko micro/nano beams. In this paper, a predictorcorrector technique is utilized to deal with the set of nonlinear governing equations.…”

Section: Introductionmentioning

confidence: 99%

Size dependent analysis of tapered FG micro-bridge based on a 3D beam theory

2019

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In the current study, an analytical solution based on a modi ed couple stress theory for a nonlinear model describing the couple 3D motion of a functionally graded tapered micro-bridge is presented. The small scale e ects and the nonlinearity arising from the mid-plane stretching are taken into consideration. Governing equations of motion are derived utilizing modi ed couple stress theory and applying the Hamilton principle. Dynamic and static analyses to determine the e ects of lateral distributed forces and mid-plane stretching are investigated. Towards this aim, analytical the Homotopy-pade technique is employed to capture the nonlinear natural frequencies in high amplitude vibrations of tapered micro-bridges with di erent types of geometry and material composition. The obtained results of frequencies propose that there is good agreement between the present analytical results and the numerical ones, as opposed to the well-known multiple-scale method. Furthermore, comparing the results in 2D and 3D analyses shows that in 2D analysis, the sti ness and natural frequency of the micro-beam is underestimated and it is observed that increasing the tapered ratio has di erent impacts on natural frequencies for micro-beams with di erent slender ratios.

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Studying linear and nonlinear vibrations of fractional viscoelastic Timoshenko micro-/nano-beams using the strain gradient theory

Cited by 36 publications

References 45 publications

Nonlinear vibration analysis of the nanobeams subjected to magneto-electro-thermo loading based on a novel HSDT

Nonlinear vibration analysis of the nanobeams subjected to magneto-electro-thermo loading based on a novel HSDT

Investigating vibrations of viscoelastic fluid-conveying carbon nanotubes resting on viscoelastic foundation using a nonlocal fractional Timoshenko beam model

Size dependent analysis of tapered FG micro-bridge based on a 3D beam theory

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