Coupled finite element : series expansion method for the modeling of directional piezoelectric sources radiating in an elastic formation
Résumé
A numerical method is proposed to describe, in the frequency domain, the elastic waves radiated from a piezoelectric transducer in an infinite elastic formation in the rotational symmetric case. It relies upon the coupling between the Finite Element Method, to model the transducer and the surrounding formation up to a spherical boundary, and a series expansion, to model the field on and outside the boundary. Validation tests conducted on point force show that the accuracy of the results is mainly determined by the number of terms used in the series expansion which has to be increased when the frequency increases. The method is applied to the design of a directional piezoelectric source. The directional radiation is obtained by controlling electrically the symmetrical and anti-symmetrical vibrations of a double-ended longitudinal vibrator. The control law on electrical excitation is extracted from the numerical computation and a directional radiation is obtained for both longitudinal and transverse waves.