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Analytical Solutions for Nonlinear Free Vibration of Micro-Scale Timoshenko Beams

[+] Author Affiliations
Zia Saadatnia, Ebrahim Esmailzadeh

University of Ontario Institute of Technology, Oshawa, ON, Canada

Davood Younesian

Iran University of Science and Technology, Tehran, Iran

Paper No. DETC2016-60598, pp. V008T10A033; 6 pages
  • ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 8: 28th Conference on Mechanical Vibration and Noise
  • Charlotte, North Carolina, USA, August 21–24, 2016
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5020-6
  • Copyright © 2016 by ASME


Nonlinear free vibration of micro-beams based on the Timoshenko beam model is studied. The governing equations of motion using the strain gradient theory, Von Kármán strain tensors and Hamiltonian principle, are developed. The Galerkin method is applied to the governing equations and the coupled nonlinear ordinary differential equations of system are obtained. The variational iteration method is utilized to determine the time responses of the micro-beam and also a close form expression for the frequency-amplitude is found. The analytical solutions obtained for different values of parameters are compared with those found from different numerical methods. The effects of geometrical and physical parameters on the dynamics of micro-beam are also examined. Moreover, the analytical formulation for frequency ratio, i.e., the ratio of nonlinear natural frequency to the linear one is obtained and the sensitivity of this ratio to the variations of various parameters is evaluated. It is proved that the proposed solution methods and the results obtained are accurate and reliable when dynamics of such micro structures are studied.

Copyright © 2016 by ASME



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