Active vibration control of doubly tapered thin-walled beams using piezoelectric actuation

Abstract

This paper deals with a study of the modeling and open/closed-loop vibrational behavior of cantilevered beams of non-uniform cross-sections featuring non-classical properties such as transverse shear, anisotropy and heterogeneity of their constituent materials. The active feedback control capability is based upon the implementation of adaptive materials, consisting of piezoelectric layers that are bonded or embedded into the host structure and fully distributed along the entire beam span. As a result of the converse piezoelectric effect considered in conjunction with the out-of-phase activation, a boundary moment is induced at the beam tip. A combined dynamic feedback control law relating the piezoelectrically induced boundary bending moment to the various kinematical response quantities is implemented, and its effects upon the closed-loop eigenfrequencies are investigated. The results obtained reveal the high efficiency of the control methodology adopted towards enhancement of the vibrational behavior of these structures, and emphasize, in this context, the implications of the non-uniformity of the beam cross-sections considered in conjunction with other non-classical effects.