On the vibration of postbuckled functionally graded-carbon nanotube reinforced composite annular plates

This paper studies the free vibration charachterstics of post-buckled functionally graded nanocomposite annular plates reinforced by single-walled carbon nanotubes (SWCNTs). The analysis is performed by employing a generalized differenitail quadrature (GDQ)-type numerical technique and psedue arc-length continuation scheme. The SWCNT reinforcement is considered to be either uniformly distributed (UD) or functionally graded (FG) in the thickness direction. The material properties of functionally graded carbon nanotube reinforced composite (FG-CNTRC) plates are estimated using an equivalent continuum model based on the modified rule of mixture. The vibration problem is formulated on the basis of the first-order shear deformation theory for moderately thick laminated plates and von Kármán geometric nonlinearity. By employing Hamilton’s principle and a variational approach, the governing equations and the associated boundary conditions (BCs) are derived which are then discretized via the GDQ method. The postbuckling characteristics of FG-CNTRC annular plates are investigated by plotting the equilibrium postbuckling path as the load-deflection curves. Thereafter, the free vibration behavior of FG-CNTRC annular plates in pre- and post-buckled states is examined. Effects of different parameters including type of BCs, CNT volume fraction, outer radius-to-thickness ratio and inner-to-outer radius ratio are investigated in detail.