Backward propagation of sound fields radiated by impacted plates using a transient acoustical holography approach

Near-field acoustical holography can be used as a non-contact technique for time and space visualization of both sound pressure field and transverse acceleration of the source. In the present paper, the backward propagation of transient sound fields radiated by impacted plates. Time aliasing errors in reconstructed signals, encountered with Fourier transform based acoustical holography, are discussed through a simulated hologram. The standard holography method is compared to a transient formulation, which suppresses aliasing errors since it relies on numerical Laplace transforms. Backward propagation of sound pressure signals using the transient approach requires a double regularization process to filter both evanescent waves and instabilities due to the inversion of the numerical Laplace transform. The use of Tikhonov filters optimized using the L-Curve method is investigated for such applications. Finally, this approach is validated experimentally with the backward propagation of the sound pressure radiated by a free Plexiglas plate impacted by a steel pendulum.