Finite element modeling and active vibration control of high-speed spinning flexible beam

Finite element modeling and active vibration control of a high-speed spinning flexible coupled electromechanical beam is investigated using a first-order approximation coupling (FOAC) model. Due to centrifugal forces caused by eccentricity in a spinning flexible beam, there exists coupling between axial and transverse vibration modes. The partial differential equations of motion of the beam governing this coupling are derived using Hamilton's principle based on an FOAC model, and a finite element method for discretization is given. It is observed that the zero-order approximate coupling (ZOAC) model is valid for dynamic description of the flexible beam spinning at low speeds, but no longer valid at high speeds. However, the validity of FOAC model is confirmed at different speeds. Piezoelectric elements for active vibration control of the spinning flexible beam are analyzed and a velocity feedback controller is proposed. Simulation results demonstrate good performance of the proposed velocity feedback controller.