Model Order Reduction and Pass-band Based Calculations for Disordered Periodic Structures

This paper is concerned with the dynamics of disordered periodic structures. The free vibration problem is considered. A method akin to the Rayleigh method is presented. This method is particularly suitable for the study of periodic structures as it exploits the nominal periodicity leading to an approximation that greatly reduces the order of the model. The method is used to calculate the natural frequencies and mode shapes for a pass-band by treating the unknown phases between the nominally identical bays as the generalized co-ordinates of the problem. An illustrative example of a cyclically coupled beam model is presented. In spite of a very large reduction in the computational effort, the results obtained are very accurate both for frequencies and mode shapes even when strong mode localization is observed. To test the performance of the proposed approximation further, a situation where two pass-bands are brought close to each other is considered (a coupled beam model having inherent bending-torsion coupling). The method presented here is general in its formulation and has the potential of being used for more complex geometries.