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CATEGORIES:Engineering Department Dynamics and Vibration Tea
Time Talks
SUMMARY:Eigenmodes of simple elastic waveguides:shear corr
ection\, bending-torsion coupling\, and aeroelasti
city - Dr Atul Bhaskar (University of Southampton)
DTSTART;TZID=Europe/London:20110429T160000
DTEND;TZID=Europe/London:20110429T170000
UID:TALK30858AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/30858
DESCRIPTION:Abstract: In this talk\, propagating waves in elas
tic bars will be considered in the spirit of asymp
totic analysis. The case of bending-torsion coupli
ng and that of shear correction will be discussed.
The inclusion of shear deformation amounts to sin
gular perturbation of the Euler-Bernoulli (EB) fie
ld equation. Timoshenko incorrectly treated the pr
oblem as one of regular perturbation and missed ou
t one physically meaningful 'branch' of the disper
sion curve\, which is mainly shear-wise polarized.
Asymptotic formulae for dispersion\, standing wav
es\, and the density of modes will be given in ter
ms of a small pertubation parameter. The second sp
ectrum—in the light of the debate on its existence
\, or not—will be discussed. The so-called 'Timosh
enko beam equation' appears to be dubious on its o
wn and is not derivable by any known Lagrangian. F
inally\, the field equations of the bending-torsio
n coupled waveguide are modified by the inclusion
of aerodynamic forces. The equations of motion are
presented in terms of matrices explicitly depende
nt on the flow velocity. The temporal stability an
d the spatial stability are explored via a quartic
and a quadratic equation\, respectively. The prob
lem can alternatively be posed as a •-matrix probl
em and a generalised eigenproblem\, respectively.
Illustrative examples will be given.
LOCATION:Cambridge University Engineering Department\, Oatl
ey Seminar Room
CONTACT:Ms Helen Gardner
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