Nonlinear dynamic analysis of temperature-dependent functionally graded magnetostrictive sandwich nanobeams using differ
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(2020) 42:314
TECHNICAL PAPER
Nonlinear dynamic analysis of temperature‑dependent functionally graded magnetostrictive sandwich nanobeams using different beam theories A. H. Ghorbanpour‑Arani1 · M. Abdollahian2 · A. Ghorbanpour Arani2,3 Received: 26 November 2018 / Accepted: 4 May 2020 © The Brazilian Society of Mechanical Sciences and Engineering 2020
Abstract In the present study, nonlinear dynamic analysis of an embedded functionally graded sandwich nanobeam (FGSNB) integrated with magnetostrictive layers is investigated. The core layer of FGSNB, which is subjected to a time-dependent transverse load, is made of a two-constituent functionally graded material that the material properties of the functionally graded nanobeam are temperature dependent and assumed to vary in the thickness direction. The modified couple stress theory is taken into account so as to consider the small-scale effects. The surrounding elastic medium is simulated as visco-Pasternak foundation to study the effects of damping, shear and elastic effects of surrounded medium. Using energy method and Hamilton’s principle, the governing motion equations and related boundary conditions are obtained for different beam theories. Finally, the differential quadrature as well as Newmark-β methods are employed to obtain the nonlinear dynamic response of the functionally graded magnetostrictive sandwich nanobeam (FGMSNB), and therefore deflection-response curves are plotted to study the effects of small-scale parameter, surrounding elastic medium, magnetostrictive layers, geometrical parameters, material compositions of core layer, environment temperature and boundary conditions and nonlinear terms graphically. The results indicate that the magnetostrictive layers play a key role on the dynamic behavior of the FGMSNB. Moreover, comparing results with those obtained in Ghorbanpour Arani and Abdollahian (Mech Adv Mater Struct, 2017. https://doi.org/10.1080/15376494.2017.1387326) shows the importance of the nonlinear terms. The obtained results in this paper can be used as sensor and actuator in the sensitive applications. Keywords Nonlinear dynamic analysis · Magnetostrictive sandwich nanobeam · Functionally graded material · Modified couple stress theory · Visco-Pasternak medium
1 Introduction Magnetostrictive materials are known as a type of smart materials that their size, shape and magnetization changes in response to the magnetic field and mechanical stress. Considering this fact, magnetostrictive materials can be used in Technical Editor: Wallace Moreira Bessa, D.Sc. * A. Ghorbanpour Arani [email protected]; [email protected] 1
School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran
2
Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
3
Institute of Nanoscience and Nanotechnology, University of Kashan, Kashan, Iran
sensors and actuators applications. Therefore, many investigators have been selected magnetostrictive materials as a research topic. For instance, W
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