Rovetta D., Ribay G., Sarti A., De Sanctis G., Catheline S.

Tactile interactions with thin plates generate modal propagation of elastic waves that, in the frequency range of interest (0-10 kHz), is made of only the two lowest-order modes (flexural and longitudinal). Using sensors that acquire just vertical displacements, the flexural mode is, in fact, the only one that is recorded. In order to localize the interaction from the acquired signals using such sensors, we consider two classes of solutions: TDOA (Time Delay Of Arrival) and CC (localisation by Cross-Correlation). In both cases a method that predicts the response of the board to a tactile excitation would be extremely useful, as it would enable TDOA to greatly improve its accuracy; in addition, it would greatly simplify the learning phase of CC techniques. With these goals in mind, we developed two methods for predicting the board’s response. The former computes the exact flexural modal solution by setting free boundary conditions only on the interaction surfaces while assuming the plate to be of infinite extension. The plate’s borders are then accounted for through ray tracing. The latter is based on the numerical solution of the elastic wave equation, which inherently takes into account the reflections at the plate’s border. We tested and compared the two methods on real data, which proved effective on a wide range of situations. The former turned out to excel with larger plates and in the presence of weak reverberations, while the second proved more accurate in complementary situations. As both methods need to know the excitation signal and the elastic parameters of the plate, we also developed a method for computing the excitation through wave dispersion compensation based on inverse propagation, and a method for estimating the elastic parameters from the acquired data. This latter solution was validated through measurements in the ultrasonic range.