Large Amplitude Forced Vibration Analysis of Functionally Graded Carbon Nanotube-Reinforced Composite Beams

The present research aims to investigate the nonlinear forced vibration of carbon nanotube-reinforced composite (CNTRC) beams. It is assumed that the beam is subjected to a transverse periodic excitation. Uniform distribution (UD) and functionally graded (FG) distribution of single-walled carbon nanotubes (SWCNTs) are considered as the reinforcement distribution patterns in the polymeric matrix. In the FG distribution, the material properties of the nanobeam are assumed to vary in the thickness direction. The extended rule of mixture is applied to estimate effective material properties of the CNTRC beams. The governing equation is formulated based on the Euler-Bernoulli beam theory along with Hamilton’s principle. The von Kármán strain-displacement relations are also considered to apply the geometric nonlinearities. Employing the Galerkin procedure and variational iteration method, the nonlinear governing equation is solved and analytical solutions for vibrational properties of the CNTRC beams are obtained. The relevant numerical results from the literature are provided and compared with the present solution to examine the reliability and correctness of the current approach. Finally, a detailed parametric study is presented to investigate the effects of different parameters such as volume fraction, carbon nanotube distribution, dimensionless force amplitude, dimensionless damping coefficient, slenderness ratio, end supports and vibration amplitude on the nonlinear vibration frequencies and vibration response of the beams.