Resonances of an elastic plate coupled with a compressible confined flow.

Publication type:
Paper in peer-reviewed journals
Quarterly Journal of Mechanics and Applied Mathematics, vol. 62(2), pp. 105-129
The theoretical study of the resonances of an elastic plate in a compressible flow in a 2D duct is presented. Due to the fluid-structure 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 self-adjoint 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.
    author={Anne-Sophie Bonnet-BenDhia and Jean-François Mercier },
    title={Resonances of an elastic plate coupled with a compressible 
           confined flow. },
    doi={10.1093/qjmam/hbp004 },
    journal={Quarterly Journal of Mechanics and Applied Mathematics },
    year={2009 },
    volume={62(2) },