Dynamic Modeling and Analysis of a Rotating Piezoelectric Smart Beam

In active vibration control study, piezoelectric actuators and sensors are bonded on the surface of a beam. They can change the frequency and modal characteristics of the system. This paper presents an analysis of the frequency response to a rotating piezoelectric smart beam. Hamilton’s principle along with the assumed mode method are employed to derive the governing equations of the first-order approximate coupling model for the piezoelectric smart beam. The coupling is taken into account as the second-order coupling effect of the axial elongation caused by the transverse displacement of the beam. Then, the equations are transformed into a dimensionless form after identifying the necessary parameters. The dimensionless natural frequencies of the piezoelectric smart beam corresponding to the bending and stretching vibrations are obtained through a numerical simulation, with comparison made of those of the beam with no actuator or sensor. Furthermore, the implication is investigated of the structural parameters and bond location on the piezoelectric actuators and sensors. Besides, the common case of a smart beam bonded with multiple pairs of piezoelectric actuators and sensors is studied, and the effects of the first natural frequency and tip deformation are analyzed. The research provides a theoretical reference for the optimization of structural parameters and location of piezoelectric actuators and sensors, thereby preventing the resonance when the excitation frequency is approximately equal to the natural frequency of the beam.