VIBRATION ANALYSIS OF SHROUDED BLADED-DISC ASSEMBLIES

Engineering structures designed and assumed to be periodic rarely satisfy this condition in practice due to manufacturing errors or inherent minute differences in material properties. It is now known that such deviations from the ideal periodicity can give rise to unpredictable and undesirable dynamic behavior, which could even cause failure. In such cases, energy input into the nearly-periodic system can accumulate in only a some small region of the overall system, a phenomenon known as mode localization. One parameter for quantifying this phenomenon is the mode localization factor, which measures the exponential rate of energy decay from one station to the next in the nearly-periodic structure. In this paper, we investigate the dynamic behavior of linear and cyclic chains of cantilever beams, coupled by linear springs. This could, for instance, simulate the behavior of a shrouded bladed disk on a rotating shaft, where the shroud is modeled as massless linear springs. An exact solution is given for both the tuned (perfectly periodic) and mistuned (nearly periodic) cases, based on Green’s functions.