Vibration analysis of composite plates reinforced CNTs using an exponential function approach

Free vibration analysis of functionally graded material ‘FGM’ plates reinforced with carbon nanotubes (CNTs) using exponential distribution law is investigated. Nonlinear distribution through the thickness direction of Nano-fillers is considered in the present study. Thus, the mechanical properties of the nanotubes vary through the thickness and are evaluated using a modified rule of mixture. In the finite element analysis formulation, the first-order shear deformation theory has been implemented by using the exponential law. The obtained results show a better distribution of CNTs through the thickness, which leads to an improved plate stiffness. An increase in the natural frequencies is thus expected. The obtained results show the five natural frequencies which compare well with those available in the literature.