Dynamic modeling and resonant analysis of rotating internally connected laminated piezoelectric beams

In this paper, transient dynamic responses and frequency characteristics of a rotating internally connected laminated piezoelectric beam are analyzed and studied. Since the beam is compressed by the centrifugal force, frequencies decrease with the increase in the rotating speed (and centrifugal force), which can be called as the dynamic softening effect. When the frequency of increasing speed is gradually close to the decreasing the first frequency, the system resonance will occur. Nevertheless, the resonant rotating speed was rarely accurately calculated in the previous studies owing to ignoring the foreshortening effect that plays a significant role in the dynamic softening. To this end, a novel dynamic model of rotating internally connected laminated piezoelectric beams is developed. In this model, constitutive equations for metallic and piezoelectric material are considered, and the axial shortening displacement caused by the bending deformation is calculated for the foreshortening effect. The buckling rotating speeds obtained from the presented model show good agreement with those presented by the research considering the foreshortening effect, which well validates the model. Several examples are presented for investigating effects of radius, foreshortening effect, rotating speed on transient dynamic responses and frequency characteristics. The results show that beat and resonant vibrations can be orderly observed when the rotating speed is gradually close to the resonant speed. The resonant rotating speed is smaller than the buckling one. The simplified model ignoring the foreshortening effect leads to imprecise results including dynamic responses, buckling and resonant speeds.