Membrane shape and boundary conditions estimation using eigenmode decomposition

This paper investigates the problem of estimating the shape or the boundary impedance of a vibrating membrane from acoustic measurements in a limited sub-domain of the membrane. In acoustics, polygonal room shapes are usually estimated through room impulse response measurements. Impedance values of materials are, in turn, often calculated from the measurement of the acoustic reflection coefficients at the boundaries. In this work, we develop an alternative frequency-domain method to estimate the shape of a convex membrane with generalized Robin boundary conditions, from the measurement of its eigenmodes on a small portion of its surface. Reciprocally, we show that the same model allows to estimate the membrane borders' impedances when its shape is known.