Identification of fluid-borne and structure borne vibration sources from displacement measurements in immersed beams

We investigate an inverse source problem in a coupled fluid–structure interaction (FSI) framework, in which a compressible fluid occupies a rectangular domain bounded below by an elastic Euler–Bernoulli beam. The system is excited by two unknown spatial sources with known time dependence: one acting in the fluid, the other on the beam. We aim to determine both spatial components from partial measurements of the beam displacement over a finite time interval. The mathematical model consists of a coupled system of wave and beam equations with appropriate interface and boundary conditions. We establish a uniqueness result for the recovery of the source pair from restricted observations. Numerical simulations confirm the theoretical findings, highlighting the role of a minimal observation time and the sensitivity of the reconstruction to noise in the data. These results contribute to the mathematical understanding of inverse problems in vibroacoustics and provide a foundation for practical applications such as structural health monitoring and source localization.