Nonlinear modal positive position feedback for vibration control in distributed parameter systems

Abstract

Trends in manufacturing technology towards the use of lightweight materials,and the existence of refined structural design methods have made the modern structures more flexible. The dynamic response of such structures is typically characterized by low fundamental modal resonance frequencies, low structural damping,and low stiffness, which may result in severe vibrations under external disturbances. The control of low frequency noise and vibration in such structures has traditionally been difficult and expensive, because of the long acoustic wavelengths involved. A new technique of vibration suppression for flexible structures is investigated in this paper. The technique, called active Vibration Clamping Absorber (VCA), makes use of a quadratic-modal-positive-position-feedback (QMPPF)control to design a simple second-order nonlinear controller that can suppress the vibration of structures at various resonant frequencies. The proposed QMPPF strategy uses a nonlinear modal control to transfer the vibration energy from the vibrating system to an artificial sacrificial-absorber so that large-amplitude vibrations in the main structure can be clamped within tolerable limits.The VCA can be constructed by using smart structure technology such as PZT patches excited by a digital signal processor controller. Simulation and experimental results reveal that the proposed strategy is a potentially viable means for real-time control of vibration in flexible structures.