Dynamic Stability of Functionally Graded Carbon Nanotube-Reinforced Composite Beams

Abstract

This article presents a dynamic stability analysis of functionally graded nanocomposite beams reinforced by single-walled carbon nanotubes (SWCNTs) based on Timoshenko beam theory. The material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTRCs) are assumed to vary in the thickness direction and are estimated through the rule of mixture. The differential quadrature method is employed to convert the governing differential equations into a linear system of Mathieu-Hill equations from which the boundary points on the unstable regions are determined by Bolotin's method. Free vibration and elastic buckling are also discussed as subset problems. A parametric study is conducted to investigate the influences of nanotube volume fraction, slenderness ratio, and end supports on the dynamic stability characteristics of FG-CNTRC beams. Numerical results for composite beams reinforced by uniformly distributed carbon nanotube are also provided for comparison.

Keywords:

• dynamic stability
• free vibration
• buckling
• functionally graded materials
• nanocomposites
• Timoshenko beam theory

Acknowledgments

The first author is grateful for the financial support by the National Natural Science Foundation of China (No. 11002019) and the Ph.D. Programs Foundation of China's Ministry of Education (No. 20100009120018).