Nonlinear vibration of a nonlocal nanobeam resting on fractional order viscoelastic pasternak foundations

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

doi:10.20944/preprints201806.0259.v1

Cited by 3 publications

(2 citation statements)

References 33 publications

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“…Eyebe et al. 36 studied the nonlinear vibration of a Timoshenko beam on a fractional Pasternak foundation using the multiple scale method. Praharaj and Datta 37 investigated the dynamic response spectra of a fractionally-damped beam subjected to moving point load using modal superposition approach.…”

Section: Introductionmentioning

confidence: 99%

Dynamic response of Euler–Bernoulli beam resting on fractionally damped viscoelastic foundation subjected to a moving point load

Praharaj

Datta

2020

Proceedings of the Institution of Mechanical Engineers, Part C:

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The dynamic behaviour of an Euler–Bernoulli beam resting on the fractionally damped viscoelastic foundation subjected to a moving point load is investigated. The fractional-order derivative-based Kelvin–Voigt model describes the rheological properties of the viscoelastic foundation. The Riemann–Liouville fractional derivative model is applied for a fractional derivative order. The modal superposition method and Triangular strip matrix approach are applied to solve the fractional differential equation of motion. The dependence of the modal convergence on the system parameters is studied. The influences of (a) the fractional order of derivative, (b) the speed of the moving point load and (c) the foundation parameters on the dynamic response of the system are studied and conclusions are drawn. The damping of the beam-foundation system increases with increasing the order of derivative, leading to a decrease in the dynamic amplification factor. The results are compared with those using the classical integer-order derivative-based foundation model. The classical foundation model over-predicts the damping and under-predicts the dynamic deflections and stresses. The results of the classical (integer-order) foundation model are verified with literature.

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Section: Introductionmentioning

confidence: 99%

Dynamic response of Euler–Bernoulli beam resting on fractionally damped viscoelastic foundation subjected to a moving point load

Praharaj

Datta

2020

Proceedings of the Institution of Mechanical Engineers, Part C:

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“…Recently, using nonlocal approach, Eyebe et al. 31 reported vibration of nonlinear nanobeam embedded on noninteger-order viscoelastic Winkler Pasternak-type foundation. On the other hand, Cajic et al.…”

Section: Introductionmentioning

confidence: 99%

Mathematical modeling of a fractionally damped nonlinear nanobeam via nonlocal continuum approach

Jha

Dasgupta

2019

Proceedings of the Institution of Mechanical Engineers, Part C:

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Modeling of fractionally damped nanostructure is extremely important because of its inherent ability to capture the memory and hereditary effect of several viscoelastic materials extensively used in nanotechnology. The nonlinear free vibration characteristics of a simply-supported nanobeam with fractional-order derivative damping via nonlocal continuum theory are studied in this article. Using Newton’s second law, the equation of motion for the nanobeam embedded in a viscoelastic matrix is derived. The Galerkin method is employed to transform the integro-partial differential equation of motion into a Duffing-type nonlinear ordinary differential equation. The fractional-order damping term is replaced by a combination of linear damping and linear stiffness term. The approximate analytical solution obtained via method of averaging is found to be in good agreement with solution obtained through numerical scheme. Detailed study of system parameters reveals that the fractional-order derivative damping has significant influence on the time response and effective natural frequency of the nanobeam.

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Fractional-Order Control Techniques for Renewable Energy and Energy-Storage-Integrated Power Systems: A Review

et al. 2023

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The worldwide energy revolution has accelerated the utilization of demand-side manageable energy systems such as wind turbines, photovoltaic panels, electric vehicles, and energy storage systems in order to deal with the growing energy crisis and greenhouse emissions. The control system of renewable energy units and energy storage systems has a high effect on their performance and absolutely on the efficiency of the total power network. Classical controllers are based on integer-order differentiation and integration, while the fractional-order controller has tremendous potential to change the order for better modeling and controlling the system. This paper presents a comprehensive review of the energy system of renewable energy units and energy storage devices. Various papers are evaluated, and their methods and results are presented. Moreover, the mathematical fundamentals of the fractional-order method are mentioned, and the various studies are categorized based on different parameters. Various definitions for fractional-order calculus are also explained using their mathematical formula. Different studies and numerical evaluations present appropriate efficiency and accuracy of the fractional-order techniques for estimating, controlling, and improving the performance of energy systems in various operational conditions so that the average error of the fractional-order methods is considerably lower than other ones.

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Nonlinear vibration of a nonlocal nanobeam resting on fractional order viscoelastic pasternak foundations

Cited by 3 publications

References 33 publications

Dynamic response of Euler–Bernoulli beam resting on fractionally damped viscoelastic foundation subjected to a moving point load

Dynamic response of Euler–Bernoulli beam resting on fractionally damped viscoelastic foundation subjected to a moving point load

Mathematical modeling of a fractionally damped nonlinear nanobeam via nonlocal continuum approach

Fractional-Order Control Techniques for Renewable Energy and Energy-Storage-Integrated Power Systems: A Review

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