An Optimal Control Approach to Minimum-Weight Vibrating Beam Design

ABSTRACT

A gradient projection algorithm is applied to a class of vibrating cantilever beam optimization problems which are formulated as optimal control problems. The cross-section area is distributed along the beam for minimum total weight subject to fixed natural frequency constraints and a minimum allowed area limit. Three topics receive major emphasis: the effects of shear deformation and rotary inertia, higher-mode frequency constraints, and multiple frequency constraints. Computational results are presented for the cases of fixed fundamental frequency, fixed second-mode frequency, and fixed fundamental and second-mode frequencies under a variety of conditions.