On the vibrational behavior of variable thickness FG porous beams with graphene-reinforced nanocomposite facesheets

This study delves into the vibrational behavior of a variable thickness sandwich beam which rests on a three-parameter elastic foundation. The beam’s thickness gradually decreases along its length. The core of the sandwich beam is made from functionally graded porous materials, and the facesheets are reinforced by graphene nanoplatelets. As the distribution pattern of these reinforcements varies with the beam's height, stress transformations at specific angles are necessary to compute the equivalent properties of the materials. Through the utilization of Hamilton's principle and a variational approach, the governing motion equations and the corresponding boundary conditions are deduced. Generalized differential quadrature method as a powerful numerical scheme is employed solve the derived equations under various combinations of boundary conditions to analyze the effects of parameters such as geometry, porosity coefficient, various distribution porosity and graphene dispersion patterns, and the angle of transformation on the natural frequencies.