Dynamic behaviour of axially moving nanobeams based on nonlocal elasticity approach

Abstract

In this article, transverse free vibrations of axially moving nanobeams subjected to axial tension are studied based on nonlocal stress elasticity theory. A new higher-order differential equation of motion is derived from the variational principle with corresponding higher-order, non-classical boundary conditions. Two supporting conditions are investigated, i.e. simple supports and clamped supports. Effects of nonlocal nanoscale, dimensionless axial velocity, density and axial tension on natural frequencies are presented and discussed through numerical examples. It is found that these factors have great influence on the dynamic behaviour of an axially moving nanobeam. In particular, the nonlocal effect tends to induce higher vibration frequencies as compared to the results obtained from classical vibration theory. Analytical solutions for critical velocity of these nanobeams when the frequency vanishes are also derived and the influences of nonlocal nanoscale and axial tension on the critical velocity are discussed.