Preprint Article Version 1 This version is not peer-reviewed

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

Version 1 : Received: 12 June 2018 / Approved: 15 June 2018 / Online: 15 June 2018 (14:48:29 CEST)

A peer-reviewed article of this Preprint also exists.

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. 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.

Journal reference: Fractal Fract 2018, 2, 21
DOI: 10.3390/fractalfract2030021

Abstract

In the present study, nonlinear vibration of a nanobeam resting on fractional order viscoelastic Winkler-Pasternak foundaion is studied using nonlocal elasticity theory. 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. Detailled parametric study is conducted, the effects of variation in 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 significant effect on the natural frequency and the amplitude of vibrations

Subject Areas

Nanobeam; fractional-order; nonlinearity; Winkler-Pasternack

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