Analytical and experimental analysis of Lamb wave generation in piezoelectrically driven Timoshenko beam

Abstract

Piezoelectric-generated Lamb wave in a Timoshenko beam is studied, analytically, experimentally, and using finite element simulation in this article. The governing equations of the beam with the piezoelectric patches are derived based on integration of the piezoelectric transducer vibration equations into the vibration equations of the Timoshenko beam structure. Finite element model of the beam and the piezoelectric patches is then developed in which the Rayleigh damping factors have been estimated using modal analysis. The results obtained by proposed analytical and finite element models are compared with experimental ones. A significant agreement has been observed and three principal sets of signals have been distinguished by experimental, analytical, and finite element method results: the direct emitted waves and reflected waves from the clamped and tip boundaries. The velocity of wave propagation in a brass beam is determined about 4800 m/s with the actuation frequency of 200 kHz using Lamb wave propagation signals. The results show that exciting the structure in high frequency prevents to overlap the emitted waves from the actuator and reflected waves from the boundaries in short structures.