The geometrically nonlinear forced vibration response of magneto-electro-thermo-elastic (METE) rectangular plates is analyzed herein using a numerical approach. The shear deformation effect is taken into account based on the first-order shear deformation plate theory. The geometrical nonlinearity is also considered using the von Kármán hypothesis. Based upon a variational approach, the energy functional of problem is obtained and represented in matrix form. Then, the variational differential quadrature technique is utilized to directly discretize that functional. For the solution in the time domain, the time periodic discretization method is employed. Finally, the pseudo arc-length continuation technique is used to find the frequency-response curves of METE plates under various boundary conditions. The influences of electric voltage, magnetic potential and temperature difference on the primary resonant dynamics of METE plates are investigated.

中文翻译：

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磁电热弹性板初级共振动力学的数值研究

本文使用数值方法分析了磁电热弹性 (METE) 矩形板的几何非线性受迫振动响应。基于一阶剪切变形板理论考虑剪切变形效应。还使用 von Kármán 假设考虑几何非线性。基于变分方法，获得问题的能量函数并以矩阵形式表示。然后，利用变分微分正交技术直接离散该函数。对于时域中的解，采用时间周期离散化方法。最后，采用伪弧长延拓技术求出METE板在各种边界条件下的频响曲线。电压的影响，