Reverberation of flexural waves scattered by a local heterogeneity in a plate.

A statistical model is proposed to relate the scattering properties of a local heterogeneity in a plate to the statistical properties of scattered and reverberated flexural waves. The contribution of the heterogeneity is isolated through the computation of differential signals consisting of a subtraction of the signals recorded after and before introduction of the heterogeneity. The theoretical expression of the average reverberation envelope of these differential signals is obtained as a function of the scattering cross-section of the heterogeneity.

Extraction of statistical properties of the point source response of a reverberant plate and application to parameter estimation (L).

The point source response of a reverberant solid plate is modeled through a nonstationary Poisson process based on the image-source method. The theoretical expectation of the envelope is then derived, taking into account the dispersive nature of plate waves, and validated by numerical results. Least-square curve-fitting applied to an ensemble average over N realizations can then be used to identify useful parameters such as wave velocity, plate surface, or source-receiver distance.