Non-linear vibration suppression of a composite panel subject to random acoustic excitation using piezoelectric actuators

A coupled structural–electrical finite element model for the active control of the non-linear vibration of a composite panel bonded with piezoelectric materials under random excitation is presented in this paper. The von Karman non-linear strain–displacement relations for large deflection responses and linear piezoelectricity constitutive relations are employed. A new non-linear modal finite element formulation is developed for symmetrical vibration that differs from the models in previous studies in that the first-order non-linear terms, which depend on the unknown transverse displacement, are eliminated. The system equations of motion are transformed into a set of non-linear equations in modal coordinates. The advantage of this non-linear modal transformation method is that the sizes of the non-linear matrices are reduced drastically. The transformed system equations are then written in the state space format. Four different control methods—velocity feedback, lead, lag, and H∞H∞—are employed and examined for cases of small- and large-amplitude vibrations. The effects of truncated modes on the control performance and comparisons of the control methods are studied.