Flexural vibration behavior of piezoelectric heterogeneous bimorph beams

Bending oscillations of piezoelectric bimorph beams are effective sound sources in gases or fluids and therefore of practical interest. On the basis of the piezoelectric constitutive relations and the elastodynamic equations the differential equation of flexural vibrations of thin rectangular piezoelectric heterogeneous bimorph beams consisting of a piezoelectric layer glued onto an elastic substrate is derived. The piezoelectric layer is polarized in thickness direction and can be excited to thickness vibrations by an electric ac voltage applied to electrodes covering the upper and lower surface of the layer. This causes an oscillating transverse contraction in the piezoelectric layer but not in the substrate and thus generates flexural vibrations of the beam. The differential equation is solved analytically for beams of finite length with both ends free, one clamped and one free end, and also for both ends clamped. Their vibration behavior in viscous fluids is considered. For a piezo-ceramic composite layer joined to a steel plate vibrating in air and in water the analytical results are evaluated numerically as function of frequency.