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Effect of size dependency on in-plane vibration of circular micro-rings

Karimzadeh, A ; Sharif University of Technology | 2017

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  1. Type of Document: Article
  2. DOI: 10.24200/sci.2017.4289
  3. Publisher: Sharif University of Technology , 2017
  4. Abstract:
  5. In this paper, based on the modified couple stress theory, the size-dependent dynamic behavior of circular rings on elastic foundation is investigated. The ring is modeled by Euler-Bernoulli and Timoshenko beam theories, and Hamilton's principle is utilized to derive the equations of motion and boundary conditions. The formulation derived is a general form of the equation of motion of circular rings and can be reduced to the classical form by eliminating the size-dependent terms. On this basis, the size-dependent natural frequencies of a circular ring are calculated based on the non-classical Euler-Bernoulli and Timoshenko beam theories. The findings are compared with classical beam theories. Response of the micro-ring under application of static and dynamic loads is investigated and compared with the classical theories. Results show that when the thickness of the ring is in the order of the length scale of the ring material, the natural frequencies evaluated using the modified couple stress are considerably more than those predicted based on the classical beam theories, while the deflection and natural frequencies of the classical and non-classical beam theories approach one another for the rings with thickness much larger than the material length scale. © 2017 Sharif University of Technology
  6. Keywords:
  7. Micro-ring ; Modified couple stress theory ; Resonant frequency ; Dynamic loads ; Natural frequencies ; Particle beams ; Classical beam theory ; Hamilton's principle ; Material length scale ; Microrings ; Modified couple stress ; Modified couple stress theories ; Static and dynamic loads ; Timoshenko beam theory ; Equations of motion
  8. Source: Scientia Iranica ; Volume 24, Issue 4 , 2017 , Pages 1996-2008 ; 10263098 (ISSN)
  9. URL: http://scientiairanica.sharif.edu/article_4289.html