Theoretical modeling and dynamics analysis of a rotating piezoelectric laminated beam with different setting angles

Dynamics modeling and analysis of a rotating piezoelectric laminated beam (RPLB) considering the effect of the setting angle is presented in this paper. The rotating piezoelectric energy harvester can be simplified as a RPLB which is fixed at a rotating hub. It is easy to know that a steady transversal deformation would be produced due to the transversal component of centrifugal force when the beam is not along the radial direction (the setting angle is not equal to 0° or 180°). However, the variation of steady transversal deformation and its effect were rarely considered by existing theoretical models about the rotating harvesters. To this end, a novel nonlinear dynamics model of the RPLB is developed by the combination of floating frame reference (FFR) and absolute nodal coordinate formulation. In the model, the position coordinates and gradients on the FFR are used as the nodal coordinates to describe deformation field. The enthalpy, elastic and kinetic energies of the RPLB are derived with consideration of the piezoelectric constitutive equation and the rotation of the FFR. Thus, the dynamics equations of the RPLB can be developed by using the Lagrange's equations of second kind. The results obtained from the model show agreement with those obtained from the previous literatures, which verifies the correctness of the model. Several examples are presented to analyze the effects of rotating speed, setting angle and tip mass on steady transversal deformation, output voltage and modal characteristics.