A correction method for large deflections of cantilever beams with modal approach

Abstract

Abstract. Modal based reduced order models are preferred for modelling structures in engineering problems due to their computational efficiency. One of the important limitations of the classic modal based models is that they are linear and thus can not fully account for the nonlinearities in structures. This study proposes a fast correction method to account for geometric nonlinearities linked to large deflections in cantilever beam-like engineering structures. The large deflections cause secondary motions such as axial and torsional motions when the structures go through bending deflections. The method relies on pre-computed correction terms and thus adds negligibly small extra computational cost to the time domain analyses of the dynamic response. The accuracy of the method is examined on a straight beam benchmark model and an engineering wind blade model for the IEA 15 MW wind turbine. The results show that the proposed method increases the accuracy of modal approach significantly in estimating the secondary motions in comparison to the conventional modal based linear models.