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SUMMARY:Eigenmodes of simple elastic waveguides:shear correction\, bending
 -torsion coupling\, and aeroelasticity - Dr Atul Bhaskar (University of So
 uthampton)
DTSTART:20110429T150000Z
DTEND:20110429T160000Z
UID:TALK30858@talks.cam.ac.uk
CONTACT:Ms Helen Gardner
DESCRIPTION:Abstract: In this talk\, propagating waves in elastic bars wil
 l be considered in the spirit of asymptotic analysis. The case of bending-
 torsion coupling and that of shear correction will be discussed. The inclu
 sion of shear deformation amounts to singular perturbation of the Euler-Be
 rnoulli (EB) field equation. Timoshenko incorrectly treated the problem as
  one of regular perturbation and missed out one physically meaningful 'bra
 nch' of the dispersion curve\, which is mainly shear-wise polarized. Asymp
 totic formulae for dispersion\, standing waves\, and the density of modes 
 will be given in terms of a small pertubation parameter. The second spectr
 um—in the light of the debate on its existence\, or not—will be discus
 sed. The so-called 'Timoshenko beam equation' appears to be dubious on its
  own and is not derivable by any known Lagrangian. Finally\, the field equ
 ations of the bending-torsion coupled waveguide are modified by the inclus
 ion of aerodynamic forces. The equations of motion are presented in terms 
 of matrices explicitly dependent on the flow velocity. The temporal stabil
 ity and the spatial stability are explored via a quartic and a quadratic e
 quation\, respectively. The problem can alternatively be posed as a •-ma
 trix problem and a generalised eigenproblem\, respectively. Illustrative e
 xamples will be given.
LOCATION:Cambridge University Engineering Department\, Oatley Seminar Room
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