# OPTIMIZATION OF THE NATURAL FREQUENCIES OF EULER-BERNOULLI BEAMS

## Palavras-chave:

Parametric Optimization, Genetic Algorithm, Finite Element Method## Resumo

Various types of engineering structures are subject to periodic loading such as offshore plat-

form parts and wind turbine blades. One of the main causes of failure in these structures is due to the

resonance effect, when the frequency of external loading coincides with some natural frequency of the

structure. Therefore, the maximization of natural frequencies is an increasingly sought-after topic in the

design of these components. In this paper a genetic algorithm is developed to maximize natural frequen-

cies of Euler-Bernoulli beams. Genetic algorithms are stochastic search methods, which are based on

biological concepts of adaptation, natural selection, fitness and evolution, to solve optimization prob-

lems. A beam population is created, each of them discretized in a mesh of cylindrical elements with

different diameters, initially random. The natural frequencies of the beam are found by the Finite Ele-

ment Method, and the one with the highest natural frequency creates a new generation of offsprings. In

each offspring is applied a mutation scheme that changes the diameter of any random element, making

the entire population change. So over the generations the algorithm finds out the best diameter combina-

tion that maximizes the natural frequency of the beam. Results present different shapes are obtained for

several boundary conditions and different natural frequencies maximized.