Free vibration analysis of annular sector sandwich plates with FG-CNT reinforced composite face-sheets based on the Carrera’s Unified Formulation

Abstract

This paper presents an investigation of the free vibration of annular sector sandwich plates with carbon nanotube reinforced face-sheets and various edges boundary conditions. It is assumed that carbon nanotubes are radially aligned and distributed uniformly (UD) or functionally graded (FG) in the thickness direction. The effective material properties of CNT reinforced face-sheets are estimated using the extended rule of mixture, which contains efficiency parameters to consider the size-dependent material properties. A variable kinematic model which has been utilized for FGM cases is extended to FG-CNTs to describe the continuous variation of properties through the thickness. In this paper, the Carrera’s Unified Formulation (CUF) is developed for the analysis of asymmetric sector plates for the first time. The governing equations and associated boundary conditions are obtained employing the Principle of Virtual Displacements (PVDs) based on the CUF and solved using the generalized differential quadrature (GDQ) method. Numerical results for some special cases are presented and validated by comparison with available results in the literature. Some numerical results are tabulated to show the effects of the volume fraction of carbon nanotubes, boundary conditions and geometrical parameters on the free vibration behavior of the annular sector sandwich structures with CNTRC face-sheets.