Modification of the Natural Frequency Pattern of a Cantilever Beam using Shape Optimization Method

In this paper, a cantilever beam is geometrically modified in order to equate the natural frequencies to a predefined frequency pattern. In contrast to the conventional optimization works that only improve the first natural frequency the aim is to modify several number of natural frequencies simultaneously. The developed differential evolution (DE) optimization method applies variable thicknesses to modify structural configuration of the simple cantilever beam. The core of the algorithm is a finite element method (FEM) developed with appropriate one-dimensional element. The natural frequencies obtained from the FEM model are considered as the multi-objective function in the optimization process. The validity of the results is investigated by an experimental test; a machined aluminum beam is experimentally tested by piezoelectric actuators and the desired natural frequencies are extracted. The ultimate results, limitation and efficiency of the applied algorithm are then discussed.