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Math. Comput. Appl. 2016, 21(1), 3; https://doi.org/10.3390/mca21010003

Nonlinear Vibration of a Nanobeam on a Pasternak Elastic Foundation Based on Non-Local Euler-Bernoulli Beam Theory

1,* and
1
Vocational School of Technical Sciences in Gaziantep, University of Gaziantep, Gaziantep 27310, Turkey
2
Department of Mechanical Engineering, Faculty of Engineering, Celal Bayar University, Yunusemre 45140, Manisa, Turkey
*
Author to whom correspondence should be addressed.
Received: 16 October 2015 / Revised: 23 February 2016 / Accepted: 1 March 2016 / Published: 7 March 2016
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Abstract

In this study, the non-local Euler-Bernoulli beam theory was employed in the nonlinear free and forced vibration analysis of a nanobeam resting on an elastic foundation of the Pasternak type. The analysis considered the effects of the small-scale of the nanobeam on the frequency. By utilizing Hamilton’s principle, the nonlinear equations of motion, including stretching of the neutral axis, are derived. Forcing and damping effects are considered in the analysis. The linear part of the problem is solved by using the first equation of the perturbation series to obtain the natural frequencies. The multiple scale method, a perturbation technique, is applied in order to obtain the approximate closed solution of the nonlinear governing equation. The effects of the various non-local parameters, Winkler and Pasternak parameters, as well as effects of the simple-simple and clamped-clamped boundary conditions on the vibrations, are determined and presented numerically and graphically. The non-local parameter alters the frequency of the nanobeam. Frequency-response curves are drawn. View Full-Text
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MDPI and ACS Style

Togun, N.; Bağdatlı, S.M. Nonlinear Vibration of a Nanobeam on a Pasternak Elastic Foundation Based on Non-Local Euler-Bernoulli Beam Theory. Math. Comput. Appl. 2016, 21, 3.

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