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.

在本研究中，研究了集成磁致伸缩层的嵌入式功能梯度三明治纳米束（FGSNB）的非线性动力学分析。FGSNB的核心层受到时间相关的横向载荷，它是由两成分的功能梯度材料制成的，该功能梯度纳米束的材料属性与温度有关，并且假定其厚度方向有所变化。考虑了改进的耦合应力理论，以考虑小尺度效应。将周围的弹性介质模拟为粘滞-帕斯泰纳克基础，以研究周围介质的阻尼，剪切和弹性效应。利用能量法和汉密尔顿原理，得到了不同梁理论的控制运动方程和相关的边界条件。最后，利用微分求积法和Newmark-β方法获得功能梯度磁致伸缩夹层纳米束（FGMSNB）的非线性动力响应，因此绘制了挠度-响应曲线以研究小尺度参数对周围弹性介质的影响，磁致伸缩层，几何参数，核心层的材料组成，环境温度和边界条件以及非线性项。结果表明，磁致伸缩层在FGMSNB的动态行为中起关键作用。此外，将结果与在Ghorbanpour Arani和Abdollahian中获得的结果进行比较（Mech Adv Mater Struct，2017.https：//doi.org/10.1080/15376494.2017.1387326）显示了非线性项的重要性。