Nonlinear Vibration of a Nonlocal Nanobeam Resting on Fractional-Order Viscoelastic Pasternak Foundations

Eyebe, Guy Joseph; Betchewe, Gambo; Mohamadou, Alidou; Kofané, Timoléon Crépin

doi:10.3390/fractalfract2030021

Cited by 18 publications

(8 citation statements)

References 42 publications

(56 reference statements)

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“…Here, we can notice that for the weakly nonlinear case an increase of the nonlocal parameter decreases the amplitudes and slightly bends the amplitude curves to the right (nonlinear hardening effect). This decrease of amplitude due to an increase of the nonlocal parameter is attributed to the softening effect of the nonlocal parameter, which is also confirmed in the literature[29]. The frequency shift that is visible in the validation study cannot be seen here since the lover axis represents the detuning parameter in the vicinity of the resonant frequency and not the excitation frequency itself.…”

supporting

confidence: 83%

“…Next, instead of the previous one, the Caputo definition of fractional-order derivative is used to derive the relations for the IHBM. It should be noted that the model adopted here is similar to those presented by Eyebe et al 29 but yet with the slightly different equation for the fractional visco-Pasternak foundation and numerical analysis for the strongly nonlinear case.…”

Section: Preliminariesmentioning

confidence: 99%

“…In [28], this methodology was extended to study linear and nonlinear vibrations of fractional viscoelastic Timoshenko nanobeams considering surface energy effect. However, multiple scales (MS) perturbation method was employed by Eyebe et al [29] to study the steady-state frequency response of a nonlinear nanobeam system resting on the fractional-order viscoelastic Winkler-Pasternak foundation. Farhatnia et al [30] studied buckling of FG plate resting on Pasternak elastic layer using differential transform method.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear superharmonic resonance analysis of a nonlocal beam on a fractional visco-Pasternak foundation

Nešić¹,

Cajić

Karličić

et al. 2020

Proceedings of the Institution of Mechanical Engineers, Part C:

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This paper investigates the dynamic behavior of a geometrically nonlinear nanobeam resting on the fractional visco-Pasternak foundation and subjected to dynamic axial and transverse loads. The fractional-order governing equation of the system is derived and then discretized by using the single-mode Galerkin discretization. Corresponding forced Mathieu-Duffing equation is solved by using the perturbation multiple time scales method for the weak nonlinearity and by the semi-numerical incremental harmonic balance method for the strongly nonlinear case. A comparison of the results from two methods is performed in the validation study for the weakly nonlinear case and a fine agreement is achieved. A parametric study is performed and the advantages and deficiencies of each method are discussed for order two and three superharmonic resonance conditions. The results demonstrate a significant influence of the fractional-order damping of the visco-Pasternak foundation as well as the nonlocal parameter and external excitation load on the frequency response of the system. The proposed methodology can be used in pre-design procedures of novel energy harvesting and sensor devices at small scales exhibiting nonlinear dynamic behavior.

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supporting

confidence: 83%

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Nonlinear superharmonic resonance analysis of a nonlocal beam on a fractional visco-Pasternak foundation

Nešić¹,

Cajić

Karličić

et al. 2020

Proceedings of the Institution of Mechanical Engineers, Part C:

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show abstract

“…Several studies have been performed for responses of beams and plates resting on elastic foundation and under moving loads [54], micro beams conveying fluid [55], and interaction with viscoelastic foundations [56].…”

Section: Introductionmentioning

confidence: 99%

A Quasi 3D Modified Strain Gradient Formulation for Static Bending of Functionally Graded Micro beams Resting on Winkler-Pasternak Elastic Foundation

Gholami

Alizadeh

2021

Scientia Iranica

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This paper presents the bending analysis of simply supported functionally graded (FG) size dependent beams based on modified strain gradient theory. The shear and normal deformations are considered in displacement field according to hyperbolic shear deformation theory. Governing equations and corresponding boundary conditions for FG micro beam are derived utilizing principle of minimum total potential energy. Mori-Tanaka homogenization scheme and the classical rule of mixture are used for prediction of material properties through the thickness.Effects of Winkler-Pasternak elastic foundation parameters are studied for different side to thickness ratios. Effects of different aspect ratios, elastic foundation parameters, power law gradient indexes and different loading conditions are investigated. The efficiency and accuracy of present model is demonstrated by comparing to the existing results in especial cases.

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“…The effects of the fractional-order on the deflection and bending moment of the plate are studied. Eyebe et al (2018) studied the nonlinear vibration of a Timoshenko beam resting on a fractional Pasternak foundation using the multiple scale method. Praharaj and Datta (2020c) investigated the dynamic response of the Euler-Bernoulli beam positioning on a fractionally damped viscoelastic foundation subjected to moving load, using Modal superposition method.…”

Section: Introductionmentioning

confidence: 99%

On the transient response of plates on fractionally damped viscoelastic foundation

Praharaj

Datta

2020

Comp. Appl. Math.

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This work underlines the importance of the application of fractional-order derivative damping model in the modelling of the viscoelastic foundation, by demonstrating the effect of various orders of the fractional derivative on the dynamic response of plates resting on the viscoelastic foundation, subjected to concentrated step load. The foundation of the plate is modelled as a fractionally-damped Kelvin-Voigt model. Modal superposition method and Triangular strip matrix approach are used to solve the partial fractional differential equations of motion. The influence of (a) fractional-order derivative, (b) foundation stiffness, and (c) foundation damping viscosity parameter on the dynamic response of the plate are investigated. Theoretical results show that with the increase in the order of derivative, the damping of the system increases, which leads to decreased dynamic response. The results obtained from the fractional-order damping model and integer-order damping model are compared. The results are verified with literature and numerical results (ANSYS).

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Nonlinear Vibration of a Nonlocal Nanobeam Resting on Fractional-Order Viscoelastic Pasternak Foundations

Cited by 18 publications

References 42 publications

Nonlinear superharmonic resonance analysis of a nonlocal beam on a fractional visco-Pasternak foundation

Nonlinear superharmonic resonance analysis of a nonlocal beam on a fractional visco-Pasternak foundation

A Quasi 3D Modified Strain Gradient Formulation for Static Bending of Functionally Graded Micro beams Resting on Winkler-Pasternak Elastic Foundation

On the transient response of plates on fractionally damped viscoelastic foundation

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