Application of Optimal Control Theory to Structural Optimization of a Rotor Blade

Basic researches concerning the hub dynamic loads reduction by structural optimization of a rotor blade are conducted. The purpose of this paper is to extend the low vibration blade design methodology proposed in the previous paper so as to be able to consistent with static blade structural optimization. The blade is modeled by a rotating cantilevered beam with a plane tapered cross section and the external load is assumed to be composed by steady and dynamic components with multiple dominant frequencies. Structural optimization is formulated as an optimal control problem to determine the optimum area distribution which contains both static and dynamic blade deformations as a function of radial position. Numerical studies are carried out for various combinations of constraint imposed on the area distribution and natural frequencies with a wide range of the rotor speed. By observing numerical results, influences of constraints on the optimum solution and the physical background for hub load reduction by structural optimization are clearly understood and rationality and usefulness of the proposed optimization procedure are ascertained.