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Shock and Vibration
Volume 19 (2012), Issue 3, Pages 251-256

Vibration of Timoshenko Beams Using Non-classical Elasticity Theories

J.V. Araújo dos Santos1 and J.N. Reddy2

1IDMEC/IST--Instituto Superior Técnico, Av. Rovisco Pais, Lisboa, Portugal
2Mechanical Engineering Department, Texas A&M University, TAMU, College Station, TX, USA

Received 17 August 2009; Revised 7 December 2010

Copyright © 2012 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper presents a comparison among classical elasticity, nonlocal elasticity, and modified couple stress theories for free vibration analysis of Timoshenko beams. A study of the influence of rotary inertia and nonlocal parameters on fundamental and higher natural frequencies is carried out. The nonlocal natural frequencies are found to be lower than the classical ones, while the natural frequencies estimated by the modified couple stress theory are higher. The modified couple stress theory results depend on the beam cross-sectional size while those of the nonlocal theory do not. Convergence of both non-classical theories to the classical theory is observed as the beam global dimension increases.