ORTHOGONALITY CONDITIONS FOR ACTIVE PLATE

The adjoint structure of the active structure isdefined, the reciprocity theorem, which is derived from the basicequations of the discrete active structure, is extended from thediscrete active structures to the continuous active structures. Theactive plate with distributed sensor and actuator is studied. Thecontrol equation and the measurement equation are presented by usingthe functions locating actuation and measurement, respectively, and theorthogonality conditions are derived with the modal shapes of theactive plate and its adjoint active plate. As a numerical example arectangular plate is evaluated to give the notes about modes andorthogonality conditions of the active plate. The orthogonalityconditions can be used to decouple the motion differential equations ofthe active plate.