The current research work analyzes dynamics of a sandwich disk which is gently thick. The mentioned sandwich structure has honeycomb core, a couple of middle layers having fibers of shape memory alloy (SMA), and a couple of external layers of multi-scaled hybrid nanocomposite (MHC) considering in-plane force. The core in the shape of honeycomb is manufactured of aluminum due to its high stiffness and less density compared with other materials. Applying energy methods called the principle of Hamilton, we obtained governing motion equations of the mentioned structure and solved them using First-order shear-deformation-theory (FSDT), as well as generalized-differential-quadrature-method (GDQM), respectively. To layers’ joint, the compatibility equations have been taken into account. Then, a parametric mathematical manipulation has been conducted to analyze the impacts of fibers of SMA, boundary conditions (BCs), internal loads, honeycomb network angle, ratio of external to internal radiuses, ratio of thickness to length of the honeycomb, weight fraction of CNTs, angle of fibers, ratio of honeycomb to face-sheet thickness on the frequency of the multi-phase sandwich disk. The outcomes derived reveal that for any amount of internal pressure and each BCs, the relation of the honeycomb’s thickness ratios to MHC layer (\({h}_{H}/{h}_{t}\)) and sandwich structure’s frequency is similar to quadratic function. Further results show that the effects of the fibers’ angle on the frequency can be ignored for larger \({h}_{H}/{h}_{t}\) amounts.

当前的研究工作是分析厚度稍厚的三明治盘的动力学。提及的夹层结构具有蜂窝状芯，具有形状记忆合金（SMA）纤维的一对中间层以及考虑面内力的多尺度混合纳米复合材料（MHC）的外部层。与其他材料相比，蜂窝状芯的刚度高，密度低，因此由铝制成。应用称为汉密尔顿原理的能量方法，我们获得了上述结构的支配运动方程，并分别使用一阶剪切变形理论（FSDT）和广义差分正交方法（GDQM）对其进行了求解。对于层的连接，已经考虑了兼容性方程。然后，已经进行了参数数学运算来分析SMA纤维，边界条件（BCs），内部载荷，蜂窝网络角度，内外半径之比，蜂窝厚度与长度之比，CNT的重量分数，纤维的角度，蜂窝与面板厚度的比率，以及多相夹心盘的频率。得出的结果表明，对于任何量的内部压力和每个BC，蜂窝的厚度比与MHC层之间的关系（蜂窝与面板厚度之比在多相夹心盘频率上的比例。得出的结果表明，对于任何量的内部压力和每个BC，蜂窝的厚度比与MHC层之间的关系（蜂窝与面板厚度之比在多相夹心盘频率上的比例。得出的结果表明，对于任何量的内部压力和每个BC，蜂窝的厚度比与MHC层之间的关系（\（{h} _ {H} / {h} _ {t} \））和三明治结构的频率类似于二次函数。进一步的结果表明，对于较大的\（{h} _ {H} / {h} _ {t} \）量，可以忽略光纤角度对频率的影响。