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Resonance frequencies and stability of two flexible permanent magnetic beams facing each other

Firouz Abadi, R. D ; Sharif University of Technology | 2012

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  1. Type of Document: Article
  2. DOI: 10.1016/j.jsv.2012.07.043
  3. Publisher: 2012
  4. Abstract:
  5. This paper aims at investigating the interaction of two flexible permanent magnet beams facing each other. The governing equations of motion are obtained based on the Euler-Bernoulli beam model along with Hamiltons principle. Assuming that the beams tips are far enough, each magnet beam is considered as a series of dipole segments and the external force and moment distributions over each beam due to the magnetic field of the other one is calculated in the deformed configuration. The transverse deflections of the beams are written as series expansions of the mode shapes of an unloaded cantilever beam and the Galerkin method is applied to determine the stability and resonance frequencies. Using the obtained model, the stability regions of the beams for both cases of opposite poles and same poles facing each other are obtained. Also the effect of magnets strength and flexibility of the beams on the stability boundaries are illustrated
  6. Keywords:
  7. Euler Bernoulli beams ; External force ; Governing equations of motion ; Hamiltons ; Mode shapes ; Moment distribution ; Permanent magnetics ; Resonance frequencies ; Series expansion ; Stability boundaries ; Stability regions ; Transverse deflection ; Equations of motion ; Facings ; Galerkin methods ; Natural frequencies ; Permanent magnets ; Stability
  8. Source: Journal of Sound and Vibration ; Volume 331, Issue 26 , 2012 , Pages 5745-5754 ; 0022460X (ISSN)
  9. URL: http://www.sciencedirect.com/science/article/pii/S0022460X1200569X