Free vibrational analysis of graphene reinforced annular composite plate using three-dimensional elasticity theory

This paper is carried out the free vibrational behavior of functionally graded polymer composite annular and circular plates reinforced with graphene nanoplatelets (GPLs) using three-dimensional elasticity theory. The weight fraction differs gradually across the thickness direction. Effective elasticity modulus of the nanocomposite has been estimated by the modified Halpin-Tsai model. Five different GPLs distribution patterns within the polymer matrix are considered.  State space first order differential equation by employing the equation of motion and constitutive relation within the framework of three-dimensional elasticity theory across the thickness direction is derived. Present approach is validated by comparing the numerical results with those reported in the literature. Influence of outer radius to thickness ratio, different GPL distribution patterns, GPLs loading and edge boundary conditions on the vibrational behavior of GPLs reinforced composite (GPLRC) circular/annular plates are studied. The results implied that GPLs with a low content can have an excellent influence on the natural frequencies of the circular and annular plate.