Wind energy structures: Modal analysis by the continuous model approach

In the present paper the continuous model method is applied to the prototype of a wind turbine tower in order to perform its modal structural analysis. This mathematical analysis is used as an alternative approach to the modal analysis method that uses discrete models. It is well known that in discrete models with high-level discretization and a large number of finite elements, several open questions on the accuracy, the convergence and the stability of the solution arise during the modal or response history analysis. In this sense, the results of the analysis by means of discrete modeling are in several cases doubtful and, therefore, a modal analysis by applying a continuous model as an effective alternative is recommended. To this end, the present paper proposes a continuous model approach to calculate the eigen-frequencies, periods and mode shapes to a wind turbine tower prototype. Starting from the equilibrium of forces on a differential element of the structure, the equation of motion of the tower is formulated and using in turn the known boundary conditions at the two ends of the wind tower, the tower eigen-problem is numerically treated and solved. The action of the higher mode-shapes is very important and may become critical in the case that the tower is subjected to strong dynamic loading (cf. e.g. wind) and simultaneously is excited by a strong seismic motion.