Forced vibration analysis of functionally graded carbon nanotube-reinforced composite plates using a numerical strategy

• Nonlinear forced vibration characteristics of FG-CNTRC Mindlin plates is studied.
• GDQ and numerical Galerkin methods and pseudo-arclength technique are used to solve the problem.
• Effects of model parameters on Nonlinear vibrations of FG-CNTRC plates are explored.

In this paper, the nonlinear forced vibration behavior of composite plates reinforced by carbon nanotubes is investigated by a numerical approach. The reinforcement is considered to be functionally graded (FG) in the thickness direction according to a micromechanical model. The first-order shear deformation theory and von Kármán-type kinematic relations are employed. The governing equations and the corresponding boundary conditions are derived with the use of Hamilton's principle. The generalized differential quadrature (GDQ) method is utilized to achieve a discretized set of nonlinear governing equations. A Galerkin-based scheme is then applied to obtain a time-varying set of ordinary differential equations of Duffing-type. Subsequently, a time periodic discretization is done and the frequency response of plates is determined via the pseudo-arc length continuation method. Selected numerical results are given for the effects of different parameters on the nonlinear forced vibration characteristics of uniformly distributed carbon nanotube- and FG carbon nanotube-reinforced composite plates. It is found that with the increase of CNT volume fraction, the flexural stiffness of plate increases; and hence its natural frequency gets larger. Moreover, it is observed that the distribution type of CNTs significantly affects the vibrational behavior of plate. The results also show that when the mid-plane of plate is CNT-rich, the natural frequency takes its minimum value and the hardening-type response of plate is intensified.

Using the generalized differential quadrature method, a Galerkin-based scheme, a time periodic discretization and pseudo-arc length continuation method, the forced vibrations of the composite plates reinforced by carbon nanotubes is investigated.Figure optionsDownload as PowerPoint slide