Abstract This paper presents an analytical approach on the nonlinear magneto-electro-elastic vibration of smart sandwich plate. The sandwich plate consists of a carbon nanotube reinforced nanocomposite (CNTRC) core integrated with two magneto-electro-elastic face sheets. For core layer, three types of carbon nanotube (CNT) distribution such as FG-O, FG-V, FG-X are considered while the volume fraction of BaTiO3 − CoFe2O4 in each face sheet is chosen to be 0.5. It is assumed that the smart sandwich plate is rested on Pasternak-type elastic foundations and subjected to the combination of external pressure, thermal, electric and magnetic loads. The coupled constitutive relations are derived based on the Hamilton's principle in which the kinematic nonlinearity is defined using Reddy's higher order shear deformation theory. The analytical solutions which satisfy the boundary conditions are assumed to have the trigonometric form. The Galerkin method is used to obtain the closed form expressions of natural frequency, the relation between the frequency ratio and dimensionless amplitude and the dynamic response of the sandwich plate. The numerical results are conducted to illustrate the effect of geometrical parameters, CNT volume fraction, temperature and moisture increment, electric and magnetic potentials on the nonlinear vibration of smart sandwich plate. The reliability of present results is evaluated by comparing with the previous results based on different approach.

中文翻译：

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湿热环境下碳纳米管增强纳米复合芯智能夹层板非线性磁电弹性振动解析解

摘要 本文提出了一种智能夹层板非线性磁电弹性振动的分析方法。夹层板由碳纳米管增强纳米复合材料 (CNTRC) 核心与两个磁电弹性面板集成而成。对于核心层，考虑了三种类型的碳纳米管 (CNT) 分布，例如 FG-O、FG-V、FG-X，同时选择每个面板中 BaTiO3 - CoFe2O4 的体积分数为 0.5。假设智能夹层板放置在 Pasternak 型弹性基础上，并承受外部压力、热、电和磁载荷的组合。耦合本构关系是基于哈密顿原理推导出来的，其中运动学非线性是使用雷迪的高阶剪切变形理论定义的。假设满足边界条件的解析解具有三角函数形式。用伽辽金法得到固有频率、频率比与无量纲幅值的关系以及夹层板的动态响应的闭式表达式。数值结果用于说明几何参数、碳纳米管体积分数、温度和水分增量、电势和磁势对智能夹层板非线性振动的影响。通过与基于不同方法的先前结果进行比较来评估当前结果的可靠性。频率比和无量纲振幅与夹层板动态响应的关系。数值结果用于说明几何参数、碳纳米管体积分数、温度和水分增量、电势和磁势对智能夹层板非线性振动的影响。通过与基于不同方法的先前结果进行比较来评估当前结果的可靠性。频率比和无量纲振幅与夹层板动态响应的关系。数值结果用于说明几何参数、碳纳米管体积分数、温度和水分增量、电势和磁势对智能夹层板非线性振动的影响。通过与基于不同方法的先前结果进行比较来评估当前结果的可靠性。