A Vibration Analysis of a Thick Micro Sandwich Panel with Metamaterial or Porous Core and Carbon Nanotubes/Graphene Platelets Reinforced Composite Based on HSDT and NSGT

In the present study, vibration analysis of thick walled sandwich panel reinforced by nanocomposite facesheets based on higher-order shear deformation (HSDT) and nonlocal strain gradient theories (NSGT) is investigated. In this work, there are all components of normal and shear strain/stress. On the other hands, the novelty of this work is to investigate general strain/stress because the sandwich structure is assumed as a thick-walled panel. Also, the current work's significance and necessity is the investigation of two-types reinforcements including carbon nanotubes (CNTs) or graphene’s platelets (GPL) with two-types cores such as porous or metamaterials [graphene origami (GOri) with negative Poisson’s ratio] to analyze vibration response of a thick-walled sandwich panel using higher order shear deformation theory (HSDT) and considering size effect based on nonlocal strain gradient theory (NSGT), thus the above highlights were not done simultaneously until now and becomes the novelty of the present work. The governing motion’s equations for the sandwich panel are obtained using the Hamilton's principle and the extended mixture rule. The effects of different parameters such as Eringen’s non-local parameter, material length scale parameter, various distributions of porosity, porosity coefficient and various distributions of CNT, volume fraction of CNT, volume fraction of GPL, weight fraction of GOri, the folding degree \(\left( {H_{Gr} } \right)\) $\left(H_{\mathit{Gr}}\right)$ and geometric dimensions of GPL on natural frequency is studied. The results of this study show that with an increase in non-local parameter and the length of structure, the natural frequency reduces and by enhancing the material length scale parameter and CNT volume fraction, the natural frequency increases because of increasing the stiffness of the structure. The functionally graded FG-X with respect to FG-O and uniform distribution (UD) has the highest natural frequency because it increases the most stiffness of sandwich panel and finally, the FG-O has the lowest natural frequency. With increasing the length and width of the GPL, the natural frequency increases and vice versa for the thickness of GPL.