Active distributed vibration control of anisotropic piezoelectric laminated plates

Abstract

Abstract A design strategy is proposed for the active vibration control of fully anisotropic plates in which the active elements are laminated, spatially distributed, piezoelectric layers. The control methodology results from stability criteria established through the second method of Lyapunov, and is based on the consideration of the total system energy. The results show that for a fully anisotropic plate it is sufficient to ensure asymptotic stability provided that three criteria are met: (1) for each piezoelectric actuator laminate above the composite structure mid-plane there exists a corresponding identically polarized sensor laminate, also located above the mid-plane; (2) a linear control law governing each conjugate sensor/actuator pair is enforced such that the input to a given actuator is always proportional and opposite in sign to the current induced by the corresponding sensor; (3) for each conjugate pair above the mid-plane there exists an identical pair below the mid-plane. The analysis shows that these design prerequisites may be relaxed significantly in the absence of bending-stretching coupling. When the design criteria are satisfied, the measure of active vibration suppression becomes directly dependent on the choice of transducer spatial distribution functions. A weaker sufficient criterion is also identified, which could potentially be utilized to relax the design constraints further for fully anisotropic media. Previously employed design strategies for bending vibration control of beams and isotropic plates are shown to be a subclass of general anisotropic plate control theory, and often destabilizing in the presence of anisotropy.