In this article, finite-element formulation based on higher order shear deformation theory (HSDT) is proposed to evaluate the nonlinear frequency characteristics of carbon nanotube reinforced magneto-electro-elastic (CNTMEE) plates. The special emphasis has been made on investigating the effects of electro-magnetic circuits on the nonlinear coupled behaviour of CNTMEE plates, for the first time in the literature. The von-Karman type of nonlinear strain–displacement relations is assumed. The nonlinear fundamental frequencies for a given maximum transverse deflection are obtained through direct iterative method. Also, different forms of functionally graded CNT distributions are considered and compared with that of uniformly distributed CNT arrangement. Several numerical illustrations are depicted to highlight the influence of parameters such as electro-magnetic conditions, CNT volume fraction, boundary conditions, aspect ratio, length-to-thickness ratio etc. One of the major outcomes of this study is the influence of coupling fields on the nonlinear frequency response of CNTMEE plates.

中文翻译：

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使用有限元法由碳纳米管增强的功能梯度磁电弹性高阶板的非线性振动

在本文中，提出了基于高阶剪切变形理论 (HSDT) 的有限元公式来评估碳纳米管增强磁电弹性 (CNTMEE) 板的非线性频率特性。在文献中首次特别强调了研究电磁电路对 CNTMEE 板非线性耦合行为的影响。假定为 von-Karman 类型的非线性应变-位移关系。通过直接迭代法获得给定最大横向偏转的非线性基频。此外，还考虑了不同形式的功能梯度 CNT 分布，并将其与均匀分布的 CNT 排列进行比较。