Static, dynamic and natural frequency analyses of functionally graded carbon nanotube annular sector plates resting on viscoelastic foundation

Abstract

In this paper, static, dynamic and natural frequency responses of composite annular sector plate with carbon nanotubes (CNTs) reinforcements resting on viscoelastic foundation are investigated. The carbon nanotubes are considered to have uniform or functionally graded pattern in the plate thickness. Kelvin-voight model is used to model the viscoelastic foundation. To model the problem, Hamilton principle based on first shear deformation plate theory and finite element method are applied. The mechanical properties of annular sector plate composed of CNTs and polymer matrix are evaluated by using the rule of mixtures. The numerical results are obtained for investigating the effect of various factors such as distribution and volume fraction of CNTs, boundary conditions, stiffness and damping coefficients of viscoelastic foundation and sector angles on natural frequency, static and dynamic transient responses of the plate.