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Open AccessArticle

Boundary Characteristic Bernstein Polynomials Based Solution for Free Vibration of Euler Nanobeams

Department of Mathematics, National Institute of Technology Rourkela, Rourkela 769008, India
Author to whom correspondence should be addressed.
J. Compos. Sci. 2019, 3(4), 99;
Received: 14 August 2019 / Revised: 23 October 2019 / Accepted: 8 November 2019 / Published: 13 November 2019
(This article belongs to the Special Issue Feature Papers in Journal of Composites Science in 2019)
This paper is concerned with the free vibration problem of nanobeams based on Euler–Bernoulli beam theory. The governing equations for the vibration of Euler nanobeams are considered based on Eringen’s nonlocal elasticity theory. In this investigation, computationally efficient Bernstein polynomials have been used as shape functions in the Rayleigh-Ritz method. It is worth mentioning that Bernstein polynomials make the computation efficient to obtain the frequency parameters. Different classical boundary conditions are considered to address the titled problem. Convergence of frequency parameters is also tested by increasing the number of Bernstein polynomials in the simulation. Further, comparison studies of the results with existing literature are done after fixing the number of polynomials required from the said convergence study. This shows the efficacy and powerfulness of the method. The novelty of using the Bernstein polynomials is addressed in detail and solutions obtained by this method provide a better representation of the vibration behavior of Euler nanobeams. View Full-Text
Keywords: nonlocal elasticity; nanobeams; Rayleigh-Ritz method; Bernstein polynomials nonlocal elasticity; nanobeams; Rayleigh-Ritz method; Bernstein polynomials
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Karmakar, S.; Chakraverty, S. Boundary Characteristic Bernstein Polynomials Based Solution for Free Vibration of Euler Nanobeams. J. Compos. Sci. 2019, 3, 99.

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