FREE AND FORCED RESPONSE OF MISTUNED LINEAR CYCLIC SYSTEMS: A SINGULAR PERTURBATION APPROACH

✍ Scribed by G.S. Happawana; O.D.I. Nwokah; A.K. Bajaj; M. Azene

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 388 KB
• Volume: 211
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1997.1349

✦ Synopsis

The effect of small deterministic parameter perturbations on the forced response of nearly periodic structures with cyclic symmetry is investigated. The general methodology developed herein is applicable to any n-degree-of-freedom, strongly coupled cyclic system with two arbitrary and independent variations in system parameters that destroy the cyclic symmetry. The specific system studied may be regarded as a simplified model of a strongly coupled bladed disk assembly. Singular perturbation methods along with modal expansion analysis are applied to gain a physical insight into the effects of parameter perturbations on the eigenvalues, the eigenvectors as well as the forced response amplitudes. The study shows that, under appropriate conditions, the splitting and veering of eigenvalues due to mistunings or small parameter variations increases the amplitude of vibration of some blades significantly compared to what would be predicted by an analysis of the perfectly tuned system. Furthermore, modal bifurcations lead to uneven vibration amplitudes irrespective of the stiffness of the coupling springs. The variations in blade amplitudes are also found to be strongly dependent on damping, and the type of engine order excitation applied to the system for the same set of mistuning parameters.