Vibrations of axially travelling CNT reinforced beams with clamped-clamped boundary condition and an elastic support

Abstract

Vibrational analysis in engineering systems of axially travelling beams has attracted noticeable attention due to the many applications, such as in robotic manipulators, cable tramways, textile fibres, and in general when there is the axial mass transport of a continuous structure. This article studies the vibrational response of axially-travelling, functionally-graded, carbon nanotube-(CNT)-reinforced beam structures, by investigating linear gyroscopic aspects, such as Argand diagrams. The distribution of CNT fibres is assumed to vary along the thickness of the beam. The Hamilton principle is employed to obtain the coupled axial and transverse behaviour of the beam, subjected to clamped-clamped boundary condition and additionally supported by a spring. These equations of motion are then solved using the modal decomposition technique for the Coriolis-dependent axial and transverse frequencies. For verification, the results are compared to the simplified case in the literature for CNT strengthened beams with zero axial velocity, the dynamics of axially travelling beams, studies of the clamped-clamped boundary condition, and the effects on the Argand diagrams, which have been performed. The Argand diagrams are plotted to examine the effects of varying axial speed on the different linear characteristics of vibration. Variation of the volume fraction of the CNT and the spring support, has also been considered, to understand its effects on the vibration characteristics. Results produced in this article are important in assisting in the future design of engineering devices involving axially travelling systems.