A new model for anisotropic magneto-electro-elastic Mindlin plates is developed by using an extended modified couple stress theory. The equations of motion and complete boundary conditions are simultaneously obtained by a variational formulation based on Hamilton’s principle. The new anisotropic magneto-electro-elastic plate model includes the models for orthotropic and transversely isotropic magneto-electro-elastic Mindlin plates and the model for isotropic Mindlin plates, all incorporating the microstructure effect, as special cases. To illustrate the new model, the static bending and free vibration problems of a simply supported transversely isotropic magneto-electro-elastic plate are analytically solved by directly applying the general formulas derived. For the static bending problem, the numerical results reveal that the deflection, rotation, electric potential, and magnetic potential of the simply supported plate predicted by the current non-classical model are always smaller than those predicted by the classical elasticity-based model, and the differences are significant when the plate thickness is very small but is diminishing as the thickness increases. For the free vibration problem, it is found that the natural frequency predicted by the new plate model is higher than that predicted by the classical model, and the difference is quite large for very thin plates.

中文翻译：

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基于扩展修正偶应力理论的微结构相关各向异性磁电弹性Mindlin板模型

使用扩展的修正偶应力理论开发了各向异性磁电弹性 Mindlin 板的新模型。运动方程和完全边界条件是通过基于哈密顿原理的变分公式同时获得的。新的各向异性磁电弹性板模型包括正交各向异性和横向各向同性磁电弹性Mindlin 板模型和各向同性Mindlin 板模型，均作为特殊情况纳入了微结构效应。为了说明新模型，直接应用推导出的一般公式，解析解决了简支横向各向同性磁电弹性板的静态弯曲和自由振动问题。对于静态弯曲问题，数值结果表明挠度、旋转、当前非经典模型预测的简支板的电势和磁势总是小于经典弹性模型预测的，并且当板厚非常小时差异显着，但随着厚度增加。对于自由振动问题，发现新板模型预测的固有频率高于经典模型预测的固有频率，对于非常薄的板，差异相当大。