We study a new family of modified interior transmission eigenvalues for the interaction of a bounded elastic body (the target) embedded in an unbounded compressible inviscid fluid (the acoustic medium). This problem is modelled with the elastodynamic and acoustic equations in the time-harmonic regime, and the interaction of the two media is represented through the dynamic and kinematic boundary conditions; these are are two transmission conditions posed on the wet boundary that represent the equilibrium of forces, and the equality of the normal displacements of the solid and the fluid, respectively.
For such a model problem, we propose a new family of modified interior transmission eigenvalues (mITP eigenvalues), which depends on a tunable parameter $\gamma$ that can help increase the sensitivity of the eigenvalues to changes in the scatterer. We analyze the distribution of the mITP eigenvalues on the complex plane, in particular we show that they are real valued, and that they either fill the whole real line or define a discrete subset with no finite accumulation point. We also justify theoretically that they can be approximated from measurements of the far field pattern corresponding to incident plane waves by solving a collection of modified far field equations.
Furthermore, for a suitable choice of the parameter $\gamma$, our theory is more complete: it includes a proof of the discreteness of the mTIP eigenvalues, an upper bound for them, and a physical interpretation of the largest of them via a Courant min-max principle.
We finally provide numerical results for synthetic data to give an insight of the expected perfomance of the mITP eigenvalues if used as target signatures in applications.
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