Experimental and theoretical investigation of transient edge waves excited by a piezoelectric transducer bonded to the edge of a thick elastic plate

Abstract

Abstract The paper presents experimental and theoretical studies of wave phenomena accompanying transient edge waves (EW) excitation by a piezoelectric transducer attached at the edge of an elastic plate. Theoretical investigations are conducted on the basis of the three-dimensional elastodynamic theory. The boundary value problem describing non-stationary wave motion is solved with the use of integral transforms and the modal expansion technique. The asymptotic analysis with the wavenumber considered as a small or large parameter is applied to the three-dimensional problem. In the first case (long-wave vibrations) the approximate formulae for the fundamental EW s pole and corresponding residue are derived. These relations take into account the influence of the transverse shear load arising because of coupling between long-wave integral and Saint-Venant s boundary layer. In the second case (short-wave vibrations) an infinite series of poles corresponding to higher order EW is revealed. Results of numerical investigations of EW dispersion properties and waveforms are presented and used for an analysis of experimental data acquired with the use of Laser Doppler vibrometry. It is shown that the contribution of EW is predominant in the wave-field excited by the load under consideration. A good agreement between theoretical predictions and measurements is demonstrated. For the calculation of transient wave-field three different models of actuator-plate interaction are developed: in the low-frequency range the interaction is considered as a static one, while the lower and higher eigenfrequencies of the actuator are taken into account in the medium- and high-frequency ranges respectively. For the low-frequency range, an explicit analytical formula is derived for calculation of EW contribution into the transient wave-field. In the high-frequency range, the excitation of the first higher order EW is predicted by the numerical solution and observed experimentally.