Modeling and Analysis of Axial, Bending, and Torsional Vibrations of a Rotating Smart Beam With End Mass

In this study, a nonlinear axial‐bending‐torsional model of a rotating beam with a bonded piezoelectric actuator is derived based on Hamilton’s principle. The derived model takes into account the piezoelectric constitutive equations. A nondimensional discretized model is developed using the assumed modes method and represented in state‐space form to obtain the natural frequencies and mode shapes. Our focus extends beyond previous models by considering the influence of the end mass, hub radius, and rotational speed on the vibrational characteristics of the rotating piezoelectric smart beams under the centrifugal stiffening and the gyroscopic effect. The effects of these parameters are investigated solely and combined as each parameter significantly impacts the system’s vibrational behavior. The vibrational characteristics of the rotating smart beam are compared to those of a rotating conventional beam to highlight the distinctive effects of the piezoelectric material. Numerical simulations showed that torsional deflection should be considered in vibration suppression models as it changes substantially with the rotational speed and end mass due to the gyroscopic coupling. Furthermore, variations in eigenvalue loci veering and mode shapes between smart and conventional beams highlight the effect of piezoelectric material on beam dynamics, with important implications for active vibration control applications.