A comprehensive vibration analysis of rotating truncated sandwich conical microshells including porous core and GPL-reinforced face-sheets

The first-order shear deformation theory (FSDT) and modified couple stress theory (MCST) are employed in this paper to investigate the free vibrational behavior of rotating truncated conical sandwich microshells. It is assumed that the sandwich microshell is made of polymer, the core is porous, and two face sheets are reinforced with graphene nanoplatelets (GPLs). To compute the effective mechanical properties of the face sheets, the rule of mixture and Halpin-Tsai model are utilized. The equations of motion are derived using Hamilton's principle incorporating the centrifugal acceleration, the Coriolis acceleration, and the initial hoop tension. To solve the governing equations in the circumferential and meridional directions, a trigonimetric functions and the differential quadrature method (DQM) are utilized, respectively. Accuracy and convergence of the presented solution are verified, and the influence of various parameters on the backward and forward frequencies of the rotating truncated conical sandwich microshells are investigated, including different boundary conditions, geometrical characteristics of the microshell, rotational speed, material length scale parameter, porosity parameter, distribution pattern of the pores, and also mass fraction, dispersion pattern and geometrical characteristics of the GPLs (thickness-to-length and aspect ratios).