Free Vibration of Carbon Nanotube–Reinforced Composite Beams under the Various Boundary Conditions

Abstract

The goal of this chapter is to present a refined beam theory (RBT) for the free vibration analysis of carbon nanotube–reinforced composite (CNTRC) beams under various boundary conditions. Single-walled carbon nanotubes (SWCNTs) are assumed to be aligned and dispersed in a polymeric matrix with various reinforcing patterns. The material characteristics of the CNTRC beams are figured out using the rule of mixture. The equations of motion of the CNTRC beam are derived based on trigonometric shear deformation theory (TrSDT) employing Hamilton’s principle. The resulting equations are solved analytically for four different boundary conditions. The developed model is notable for not only addressing the shear deformation effect but also dealing with only three unknowns as the first-order shear deformation beam theory (FSDT) of Timoshenko without including a shear correction factor. Several comparative studies are performed to assess the correctness of the current theory. In the numerical examples, the effects of carbon nanotube volume fraction, diverse types of CNT distribution patterns, span to depth ratio, and boundary conditions on the free vibration response of CNTRC beams are investigated in detail.