Vibration control and analysis of a rotating flexible FGM beam with a lumped mass in temperature field

Based on the high-order coupling (HOC) modeling theory, vibration control of a rotating rigid-flexible coupled smart composite structure in temperature field is investigated. A flexible beam made of functionally graded materials (FGM) with a lumped mass and two piezoelectric films perfectly bonded to it is attached to a horizontal rotating hub. By using the method of assumed modes to describe the deformations of the FGM beam and piezoelectric films, the rigid-flexible coupling dynamic equations of the system with the high order geometric nonlinear terms are derived via employing Lagrange’s equations. A PD controller is used in the vibration control of the system. Simulation results indicate that the intense thermally induced vibrations of the FGM beam along the longitudinal and transverse direction are efficiently suppressed after the piezoelectric active control effect works. The HOC model is more accurate than the previous low order coupled (LOC) model when the temperature gradient increases. The influence of high-order nonlinearity in the present HOC model on the characteristics of dynamics and control of flexible structures should not be ignored. The effect of temperature variation on the free vibration characteristics of the rotating smart structure is gentle despite non-negligibility.