The aim of this paper is to optimize the thickness variation function of simply supported and cantilever beams, in terms of maximizing gaps between chosen neighboring frequencies, and to analyze the obtained results. The optimization results are examined in terms of achieving the objective function (related to eigenvalue problems), but also in terms of their dynamic stiffness (forced vibrations excited by a point harmonic load). In the optimization process, a genetic algorithm was used. Problems related to structural dynamics were solved by FEM implementation into the algorithm. Sample results were presented, and the developed algorithm was analyzed in terms of the results convergence by examining several variable parameters. The authors demonstrated the validity of applying the described optimization tool to the presented problems. Conclusions were drawn regarding the correlation between stiffness and mass distribution in the optimized beams and the natural frequency modes in terms of which they were optimized.
Keywords: band gaps; beams; dynamic analysis; eigenvalue problem; finite element method; genetic algorithms; optimization.