On the free vibrations of FG-GPLRC folded plates using GDQE procedure

Abstract

The present study theoretically investigates the performance of the generalized differential quadrature element (GDQE) method to obtain the free vibration response of folded plates. The considered folded plate is assumed as a laminated functionally graded composite augmented with graphene platelets (GPLs). This kind of composite is identified as the FG-GPLRC structure. Each lamina is strengthened with randomly oriented and uniformly distributed GPLs. The GPL weight fraction of each layer changes based on several functionally graded (FG) models. The effective Young modulus of each ply is calculated utilizing a second-order correlation homogenization technique called Halpin–Tsai. Based on the GDQE method, the folded plate is split into two plate elements. The motion equations of each element are derived based on the first-order shear deformation theory and utilizing Hamilton’s principle. Equations of motion for each element are solved by employing the conventional GDQ method. After that, the suitable continuity conditions are applied to the common boundaries of the two elements. In this research, the influences of plate dimensions, crank angle, FG patterns, boundary conditions, and GPL weight fraction on the natural frequencies and corresponding mode shapes are examined.