Membrane Shape And Boundary Conditions Estimation Using Eigenmode Decomposition
Résumé
This paper investigates the problem of estimating parameters of a membrane, such as its shape and its boundary impedance, from acoustic measurements in a limited sub-domain of the mem- brane. In acoustics, the estimation of polygonal room shapes is usually achieved thanks to room impulse responses measurements. Impedance values of materials are, in turn, often calculated from the measurement of the acoustic reflection coefficients on the bound- aries. In this work, we develop an alternative frequency-domain method to estimate the shape of a convex membrane with gener- alized Robin boundary conditions, thanks to the measurement of its eigenmodes on a small portion of its surface. Reciprocally, we show that this model allows an estimation of the impedance on the membrane borders when the shape is known.
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