Static and free vibration analysis of functionally graded CNT reinforced composite plates using trigonometric shear deformation theory

Abstract

In the present study, static and free vibration analysis of single walled functionally graded carbon nano-tube (CNTs) reinforced composite plate is carried out in the framework of trigonometric shear deformation theory. Trigonometric shear deformation theory full fills the traction free boundary condition at the top and bottom of the plate due to which it does not require shear correction factor. The Hamilton's principle is used to derive governing differential equations and the Navier's solution technique is used to obtain closed-form solution. The analytical approach is used to analyse the effect of the different span thickness ratios, volume fraction of CNTs, and distribution of CNTs on the deflection, stresses, natural frequencies, and corresponding mode shapes of CNTs reinforced composite plate. Four different types of CNTs reinforcement distribution such as, uniformly distribution (UD) and three types of functionally graded (FG) i.e. FG-O, FG-X and FG-V are selected here for the analysis. Here, the efforts are made to achieve the best possible arrangement for the reinforcement distribution that will produce the improved static and free vibration responses for the functionally graded CNTs reinforced composite plate. © 2020 Institution of Structural Engineers