Random vibrations of mistuned periodic structures

Abstract

Nearly periodic structures exhibit localized modes of vibration depending upon the ex· tent of the coupling and the disorder between their periodic components. These localized modes may cause excessive vibration amplitudes resulting in significantly higher stresses than the ones the structures have been designed to withstand. The Rayleigh-Ritz method, as employed earlier, for dynamic analysis for two-span beams could predict only the lower modes of vibration at prohibitive computational expense. A semi-analytical method which predicts even the higher modes at significantly reduced cost has been applied to the free vibration analysis of two-span beams. This method has been applied to the forced vibration analysis of a couple of mistuned turbine blades modeled as a two- span beam rotating in a turbulent flow field. It is shown that the maximum vibration amplitude of the mistuned structure may increase by several hundred percent as compared to that of the perfectly ordered structure.