Vibration Analysis of Timoshenko Beam reinforced with Boron-Nitride Nanotube on Elastic Bed

In this paper, free vibration analysis of a polymer-based nano-composite beam reinforced by boron-nitride nanotubes and subjected on elastic foundation, is studied. Smooth and defect-free nanotubes with uniform and directly- orientated in matrix are intended. Also, nanotubes’ distribution in the thickness direction of beam is regarded as a uniform distribution of the three different targeted ones. The properties of nano-beam are obtained by using a micromechanical model. The governing equations based on Timoshenko beam theory are derived by using the Hamilton principle. The equations are solved by the extended differential Quadrature and the natural frequencies are obtained. The effect of various parameters such as volume fraction of nanotubes, carbon-nanotube (CNT) distribution in the thickness direction of the beam, elastic media, boundary conditions and the aspect ratio is investigated on the natural frequency. The results show that a change on these parameters has a significant impact on the natural frequency.