Theoretical and experimental study of the contribution of radial modes to the pulsed ultrasonic field radiated by a thick piezoelectric disk

Abstract

A theoretical model is presented for evaluating the transient field radiated on the axis of a thick piezoelectric disk, by vibrations propagating radially on the circular transmitting face, from its rim towards its center. We had previously considered these vibrations to account for two unexpected signals (denoted S1 and S2), which were observed by measuring, with a miniature probe, the field produced in a liquid by a barium titanate disk (25 mm in diameter, 20 mm in thickness). These signals S1 and S2, not described by the well-known piston model, are due to vibrations which propagate radially on the disk face at two different speeds (5.0 × 103 and 2.6 × 103 m/s); we have called them radial vibrations as a simplification. Here, a simulation is undertaken to explain the complex changes observed in the amplitude and in the shape of signals S1 and S2, when the distance from the disk face varies. In this theoretical approach, it is assumed that the disturbance initially located on the rim of the disk face remains unchanged during its propagation along a disk radius. With these simplifying hypotheses, different analytical expressions for the impulse velocity potential φi (t) are obtained, each of them valid in a limited area of the disk axis. The resulting transient pressure p(t) is then used to predict the signals detected by the miniature probe. For this simulation we have taken account of the time dependence of the initial motion, together with the response of the measuring device. Several plots are chosen to illustrate the influence of different parameters such as the speed of the radial vibration or the duration of the input excitation signal. Finally, the comparison with the experimental results proves the efficiency of our model to describe the main characteristics of the signals produced by the radial vibrations: their contribution is important only close to the disk face and the position of a particular point on axis, called focus, is correctly predicted. Different possible improvements in the modeling are also discussed.