Design Optimization of Beams With Multi-Layers of Corrugations

Optimal designs of beams with multi-layers of corrugations are introduced in this paper. The dynamic characteristic of corrugated structures is investigated firstly using the impedance modeling technique. The dynamic response of a beam with layers of corrugations is formulated by dividing a corrugated beam into two kinds of structural segments: one, the corrugation modeled as a curved beam using finite element method and the other, the liner treated as a straight beam formulated analytically. Then the frequency equation is derived by assembling the impedance of each structure segment based on conditions of force equilibrium and velocity compatibility. The accuracy of the impedance modeling technique are compared to different existing methods, e.g. FEM, Guyan reduction, improved reduction system (IRS), improved reduction system (DIRS), and iterative improved reduction system (IIRS). Finally, examples of optimal design of corrugated beams are presented. Results further show that with an optimal number of corrugated layers and optimal thickness of liner and medium of each layer, the corrugated beam has a desirable dynamic characteristic, e.g. the first bending natural frequency may increase 40% as compared to that of the original design.