Robust Optimal Control Applied to a Composite Laminated Beam

ABSTRACT: This paper proposes an active vibration control technique, which is based on linear matrix inequalities, that is applied to a piezoelectric actuator bonded to a composite structure, forming a so-called smart composite structure. Serendipity-type finite element, based on first-order shear deformation theory with rectangular shape, eight nodes, five mechanical degrees of freedom (DOF) per node and eight electrical DOF per piezoelectric layer, is established for the composite structural model. Additionally, a mixed theory that uses a single equivalent layer for the discretization of the mechanical displacement field and a layerwise representation of the electrical field is adopted. Temperature effects are neglected. Simulation results illustrate the effectiveness of the proposed vibration control methodology for composite structures.