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

This paper studies the free vibration characteristics of post-buckled Functionally Graded (FG) carbon nanotube (CNT) reinforced annular plates. The analysis was performed by employing a Generalized Differential Quadrature (GDQ)-type numerical technique and pseudo-arc length scheme. The material properties of FG-carbon nanotube reinforced composite (CNTRC) plates were evaluated by an equivalent continuum approach based on the modied rule of mixture. The vibration problem was formulated based on the First-order Shear Deformation Theory (FSDT) for moderately thick laminated plates and von Karman nonlinearity. By employing Hamilton's principle and a variational approach, the nonlinear equations and associated Boundary Conditions (BCs) were derived, which were then discretized by the GDQ method. The postbuckling behavior was investigated by plotting the secondary equilibrium path as the de ection-load curves. Thereafter, the free vibration behaviors of pre- and post-buckled FG-CNTRC annular plates were examined. Effects of different parameters including types of BCs, CNT volume fraction, an outer radius-to-thickness ratio, and an inner-to-outer radius ratio were investigated in detail.