Optimality conditions for a Timoshenko beam model

Abstract

Optimality conditions for a Timoshenko beam model are derived in the maximum principle. For this aim, existence and uniqueness of the solution to the beam system and controllability properties of the system are discussed. Necessary optimality condition for the beam system, subjected to the rotary damping, external excitation, and mixed integral constraints including equality or/and inequality on the control function and state, is derived in the form of maximum principle. Besides obtaining that maximum principle is necessary condition for the optimality, it is also indicated sufficient optimality requirement is maximum principle in the presence of some convexity assumptions on the constraints.