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Shock and Vibration
Volume 19, Issue 3, Pages 251-256
http://dx.doi.org/10.3233/SAV-2011-0627

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.

Citations to this Article [12 citations]

The following is the list of published articles that have cited the current article.

  • J. V. Araujo Dos Santos, and J. N. Reddy, “Free Vibration And Buckling Analysis Of Beams With A Modified Couple-Stress Theory,” International Journal of Applied Mechanics, vol. 4, no. 3, 2012. View at Publisher · View at Google Scholar
  • Ehsan Taati, Masoud Molaei Najafabadi, and J.N. Reddy, “Size-dependent generalized thermoelasticity model for Timoshenko micro-beams based on strain gradient and non-Fourier heat conduction theories,” Composite Structures, vol. 116, pp. 595–611, 2014. View at Publisher · View at Google Scholar
  • J.N. Reddy, and A.R. Srinivasa, “Nonlinear theories of beams and plates accounting for moderate rotations and material length scales,” International Journal of Non-Linear Mechanics, 2014. View at Publisher · View at Google Scholar
  • Komijani, Reddy, and Eslami, “Nonlinear analysis of microstructure-dependent functionally graded piezoelectric material actuators,” Journal of the Mechanics and Physics of Solids, vol. 63, no. 1, pp. 214–227, 2014. View at Publisher · View at Google Scholar
  • George C. Tsiatas, and Aristophanes J. Yiotis, “Size effect on the static, dynamic and buckling analysis of orthotropic Kirchhoff-type skew micro-plates based on a modified couple stress theory: comparison with the nonlocal elasticity theory,” Acta Mechanica, 2014. View at Publisher · View at Google Scholar
  • Mustafa Özgür Yayli, “Free vibration behavior of a gradient elastic beam with varying cross section,” Shock and Vibration, vol. 2014, 2014. View at Publisher · View at Google Scholar
  • C.W. Lim, G. Zhang, and J.N. Reddy, “A Higher-order nonlocal elasticity and strain gradient theory and Its Applications in wave propagation,” Journal of the Mechanics and Physics of Solids, 2015. View at Publisher · View at Google Scholar
  • S. A. H. Hosseini, and O. Rahmani, “Thermomechanical vibration of curved functionally graded nanobeam based on nonlocal elasticity,” Journal of Thermal Stresses, pp. 1–16, 2016. View at Publisher · View at Google Scholar
  • Marco Alves, and Pedro Ribeiro, “Non-Linear Modes of Vibration of Timoshenko Nanobeams Under Electrostatic Actuation,” International Journal of Mechanical Sciences, 2017. View at Publisher · View at Google Scholar
  • Pedro Ribeiro, and Olivier Thomas, “Nonlinear Modes of Vibration and Internal Resonances in Nonlocal Beams,” Journal of Computational and Nonlinear Dynamics, vol. 12, no. 3, 2017. View at Publisher · View at Google Scholar
  • A. Arbind, J.N. Reddy, and A.R. Srinivasa, “Nonlinear analysis of beams with rotation gradient dependent potential energy for constrained micro-rotation,” European Journal of Mechanics - A/Solids, 2017. View at Publisher · View at Google Scholar
  • A.V. Krysko, J. Awrejcewicz, S.P. Pavlov, M.V. Zhigalov, and V.A. Krysko, “Mathematical model of a three-layer micro- and nano-beams based on the hypotheses of the Grigolyuk-Chulkov and the modified couple stress theory,” International Journal of Solids and Structures, 2017. View at Publisher · View at Google Scholar