WAVE FINITE ELEMENT METHOD FOR THE DYNAMICS OF STRUCTURES WITH CYCLIC SYMMETRY

The finite element method for axisymmetric and cyclic symmetric structures has been developed and integrated in numerous commercial FEM codes. Based on the periodicity of the geometry and loads, the dynamics of a 3D structure can be solved by considering only its section or one period, which permits to reduce the calculation time. However, this method cannot be used easily when the boundary conditions and loads are not symmetric. This article presents a new approach of the wave finite element method (WFE) to calculate the dynamic responses of such a structure in a general case: non-symmetric loads and boundary conditions. Based on the WFE for periodic structures, we can determine the wave decomposition of a substructure's responses in the cylindrical coordinate system. The loads on the substructure can be represented as waves added to the response. Then, we apply the wave decomposition to all substructures until getting the first one and this results a relation between the wave amplitudes and the external loads. This relation is simple and can be applied for arbitrary boundary conditions via the reaction forces. The numerical results show the advantage of this methods in the calculation time in comparing with FEM.