FREE LATERAL VIBRATION ANALYSIS OF NANOBEAMS BASED ON NONLOCAL ELASTICITY BY USING WAVE APPROACH

摘要

In this paper, free lateral vibration of Euler-Bernoulli nanobeams is investigated from wave view-point. Beam is modelled using Eringen's nonlocal elasticity theory. Vibrations can be considered as travelling waves along structures. Waves propagate in a waveguide and reflect at boundaries. Firstly, propagation matrices are derived then reflection matrices for a general boundary which is made by a translational and a torsional springs are derived. Secondly, these matrices are combined to provide a concise and systematic approach to free lateral vibration analyses of nanobeams. Analytical solution for natural frequencies for arbitrary boundary conditions is derived and results are used to validate this approach. Finally small-scale effect on natural frequencies is discussed.