Energy approach vibration analysis of nonlocal Timoshenko beam theory

The aim of this paper is to present an efficient numerical method to analyze the vibration behavior of nano Timoshenko beams based on Eringen's nonlocal elasticity theory. The vibration frequencies of beams are firstly obtained using the theorem of minimum total potential energy and Chebyshev polynomial functions. The present method provides an efficient and extremely accurate vibration solution. Numerical results for a variety of some micro- and nano-beams with various boundary conditions are given and compared with the available results wherever possible. The small scale effects on the vibration frequencies of beams are determined and discussed. (C) 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of ICM11