Spectral problem from an elasto-acoustic coupling

We are interested in the theoretical study of a spectral problem arising in a physical situation, namely interactions of fluid-solid type structure, M ore precisely, we study the existence of solutions for a quadratic eigenval ue problem, which describes the vibrations of a system made up of two elast ic bodies, where a slip is allowed on their interface and which surround a cavity full of an inviscid and slightly compressible fluid. The problem sha ll be treated like a generalized eigenvalue problem. Thus by using some fun ctional analysis results, we deduce the existence of solutions and prove a spectral asymptotic behavior property, which allows us to compare the spect rum of this coupled model and the spectrum associated to the problem withou t transmission between the fluid-solid media.