Nonlinear dynamic analysis of temperature-dependent functionally graded magnetostrictive sandwich nanobeams using different beam theories

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-beta 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. 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.