Free vibrations and buckling analysis of carbon nanotube-reinforced composite Timoshenko beams on elastic foundation

This study deals with free vibrations and buckling analysis of nanocomposite Timoshenko beams reinforced by single-walled carbon nanotubes (SWCNTs) resting on an elastic foundation. The SWCNTs are assumed to be aligned and straight with a uniform layout. Four different carbon nanotubes (CNTs) distributions including uniform and three types of functionally graded distributions of CNTs through the thickness are considered. The rule of mixture is used to describe the effective material properties of the nanocomposite beams. The governing equations are derived through using Hamilton's principle and then solved by using the generalized differential quadrature method (GDQM). Natural frequencies and critical buckling load are obtained for nanocomposite beams with different boundary conditions. Effects of several parameters, such as nanotube volume fraction, foundation stiffness parameters, slenderness ratios, CNTs distribution and boundary conditions on both natural frequency and critical buckling load are investigated. The results indicate that the above-mentioned parameters play a very important role on the free vibrations and buckling characteristics of the beam.

► Beams with FG-X distribution have highest fundamental frequency.
► Beams with FG-X distribution have highest critical buckling load.
► Using elastic foundation, lead to increase the natural frequency.
► Using elastic foundation, lead to increase the critical buckling load.
► Increasing CNT volume fraction, lead to increase the natural frequency.