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Fractal Fract 2018, 2(3), 21; https://doi.org/10.3390/fractalfract2030021

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

1
Department of Physics, Faculty of Science, The University of Maroua, P.O. Box 814, Maroua, Cameroon
2
Laboratory of Mechanics, Materials and Structures, Postgraduate School in Sciences, Technology and Geosciences, Doctoral Research Unit in Physics and Applications, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon
*
Author to whom correspondence should be addressed.
Received: 12 June 2018 / Revised: 1 August 2018 / Accepted: 3 August 2018 / Published: 5 August 2018
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Abstract

In the present study, the nonlinear vibration of a nanobeam resting on the fractional order viscoelastic Winkler–Pasternak foundation is studied using nonlocal elasticity theory. The D’Alembert principle is used to derive the governing equation and the associated boundary conditions. The approximate analytical solution is obtained by applying the multiple scales method. A detailed parametric study is conducted, and the effects of the variation of different parameters belonging to the application problems on the system are calculated numerically and depicted. We remark that the order and the coefficient of the fractional derivative have a significant effect on the natural frequency and the amplitude of vibrations. View Full-Text
Keywords: nanobeam; fractional-order; nonlinearity; Winkler–Pasternak foundation nanobeam; fractional-order; nonlinearity; Winkler–Pasternak foundation
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Eyebe, G.J.; Betchewe, G.; Mohamadou, A.; Kofane, T.C. Nonlinear Vibration of a Nonlocal Nanobeam Resting on Fractional-Order Viscoelastic Pasternak Foundations. Fractal Fract 2018, 2, 21.

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