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On the geometrically nonlinear vibration of a piezo-flexomagnetic nanotube

Abstract

In order to describe the behavior of thin elements used in MEMS and NEMS, it is essential to study a nonlinear free vibration of nanotubes under complicated external fields such as magnetic environment. In this regard, the magnetic force applied to the conductive nanotube with piezo-flexomagnetic elastic wall is considered. By the inclusion of Euler-Bernoulli beam and using Hamilton’s principle, the equations governing the system are extracted. More importantly, a principal effect existed in a nonlinear behavior such as axial inertia is thoroughly analyzed which is not commonly investigated. We then consider the effects of nanoscale size using the nonlocal theory of strain gradient (NSGT). Hereafter, the frequencies are solved as semi-analytical solutions on the basis of Rayleigh-Ritz method. The piezo-flexomagnetic nanotube (PF-NT) is calculated with different boundary conditions. In order to validate, the results attained from the present solution have been compared with those available in the open literature. We realized that the nonlinear frequency analysis is so significant when a nanotube has fewer degrees of freedom at both ends, and its length is long.

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Copyright (2020 John Wiley & Sons, Ltd.)

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Category:
Articles
Type:
artykuły w czasopismach
Published in:
MATHEMATICAL METHODS IN THE APPLIED SCIENCES no. 107, pages 2411 - 2502,
ISSN: 0170-4214
Language:
English
Publication year:
2020
Bibliographic description:
Malikan M., Eremeev V.: On the geometrically nonlinear vibration of a piezo-flexomagnetic nanotube// MATHEMATICAL METHODS IN THE APPLIED SCIENCES -Vol. 107, (2020), s.2411-2502
DOI:
Digital Object Identifier (open in new tab) 10.1002/mma.6758
Verified by:
Gdańsk University of Technology

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