Cross-shaped piezoelectric beam for torsion sensing

In this paper, we introduce a cross-shaped piezoelectric beam that consists of two piezoelectric layers and polyester film as a substrate. We derive the modeling framework using the slender plate assumption to anticipate mechanical deformation caused by torsional loading. Also, we obtain a theoretical calculation of the electrical responses of the piezoelectric layers based on the mechanical deformation of a slender plate. To demonstrate the validity of the theoretical model, a series of experiments are designed to deliver torsional loadings to the cross-shaped piezoelectric beam. By comparing the amplitudes and phases of the experimental load voltages with the theoretical ones, torsional loading with various tip twisting angles and frequencies could be distinguished. In addition, we conduct a comparison between the torsional loading and the flexural loading applied to the cross-shaped piezoelectric beam. As a result, we found that the torsional loading can be differentiated from the flexural loading using the phase difference between the two piezoelectric layers. For further study, we experimentally and theoretically investigate the open-circuit voltages of the piezoelectric sensors. We observed that the open-circuit voltage amplitudes were proportional to the tip twisting angle, and remained constant with the change in frequency.