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Open AccessArticle

Buckling Behavior of Nanobeams Placed in Electromagnetic Field Using Shifted Chebyshev Polynomials-Based Rayleigh-Ritz Method

1
Department of Mathematics, National Institute of Technology Rourkela, Rourkela 769008, India
2
Department of Innovation Engineering, University of Salento, 73100 Lecce, Italy
*
Author to whom correspondence should be addressed.
Nanomaterials 2019, 9(9), 1326; https://doi.org/10.3390/nano9091326
Received: 17 July 2019 / Revised: 5 September 2019 / Accepted: 11 September 2019 / Published: 16 September 2019
(This article belongs to the Special Issue Advanced Mechanical Modeling of Nanomaterials and Nanostructures)
In the present investigation, the buckling behavior of Euler–Bernoulli nanobeam, which is placed in an electro-magnetic field, is investigated in the framework of Eringen’s nonlocal theory. Critical buckling load for all the classical boundary conditions such as “Pined–Pined (P-P), Clamped–Pined (C-P), Clamped–Clamped (C-C), and Clamped-Free (C-F)” are obtained using shifted Chebyshev polynomials-based Rayleigh-Ritz method. The main advantage of the shifted Chebyshev polynomials is that it does not make the system ill-conditioning with the higher number of terms in the approximation due to the orthogonality of the functions. Validation and convergence studies of the model have been carried out for different cases. Also, a closed-form solution has been obtained for the “Pined–Pined (P-P)” boundary condition using Navier’s technique, and the numerical results obtained for the “Pined–Pined (P-P)” boundary condition are validated with a closed-form solution. Further, the effects of various scaling parameters on the critical buckling load have been explored, and new results are presented as Figures and Tables. Finally, buckling mode shapes are also plotted to show the sensitiveness of the critical buckling load. View Full-Text
Keywords: buckling; electromagnetic field; nanobeam; shifted chebyshev polynomial; rayleigh-ritz method buckling; electromagnetic field; nanobeam; shifted chebyshev polynomial; rayleigh-ritz method
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MDPI and ACS Style

Jena, S.K.; Chakraverty, S.; Tornabene, F. Buckling Behavior of Nanobeams Placed in Electromagnetic Field Using Shifted Chebyshev Polynomials-Based Rayleigh-Ritz Method. Nanomaterials 2019, 9, 1326.

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