Title : 
Resonances of an elastic plate coupled with a compressible confined flow. 
Year : 
2009 
Type : 
paper in peerreviewed journal 
Authors : 
A.S. BonnetBenDhia, J.F. Mercier 
Abstract : 
The theoretical study of the resonances of an elastic plate in a compressible flow in
a 2D duct is presented. Due to the fluidstructure coupling a quadratic eigenvalue
problem is involved, in which the resonance frequencies k solve the equations l(k) =
k^2 where l(k) are the eigenvalues of a selfadjoint operator of the form A + kB. In
a previous paper we have already proved that a linear eigenvalue problem can be
recovered if the plate is rigid or the fluid at rest. We focus here on the general
problem for which elasticity and flow are jointly present and derive a lower bound for
the number of resonances. The expression of this bound, based on the solution of two
linear eigenvalues problems, points out that the coupling between elasticity and flow
generally reduces the number of resonances. This estimate is validated numerically. 
Themes : 
Wave guides

Reference : 
Quarterly Journal of Mechanics and Applied Mathematics  vol. 62(2) (pp 105129 ) 