Determination of the first natural frequency of vibration of a steel pole, under the effect of geometric nonlinearity, using optimization techniques / Determinação da primeira frequência natural de vibração de um pólo de aço, sob o efeito da não linearidade geométrica, utilizando técnicas de optimização

Abstract

This work aims to find a procedure to obtain an alternative formulation that represents the first mode of vibration of slender steel poles considering the effect of geometric non-linearity, using the Reyleigh-Ritz method, trigonometric formulations with optimization techniques and a finite element mathematical model. The application was on an existing polygonal steel pole. In order to consider the geometric non-linearity in the calculation of the natural frequencies of the respective structure, the concept of initial stiffness, geometric stiffness and effective stiffness, computed by the Rayleigh method for vibration problems in mechanical systems, was used. So, to optimize the computational time to obtain the modal response in dynamic analysis of the described structure, without neglecting the precision of the results of a rigorous analysis with sophisticated methodologies, alternative formulations to those described in NBR 6123 (1988) will bepresented in this work.