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

1998 ◽  
Vol 211 (5) ◽  
pp. 761-789 ◽  
Author(s):  
G.S. Happawana ◽  
O.D.I. Nwokah ◽  
A.K. Bajaj ◽  
M. Azene
Keyword(s):  
Singular Perturbation ◽  
Forced Response ◽  
Perturbation Approach ◽  
Cyclic Systems

scholarly journals Modal Analysis and Forced Response of Coupled Mistuned Cyclic Systems: A Singular Perturbation Approach

1993 ◽  
Author(s):  
G. S. Happawan ◽  
A. K. Bajaj ◽  
O. D. I. Nwokah
Keyword(s):  
Singular Perturbation ◽  
Periodic Structures ◽  
Forced Response ◽  
Perturbation Approach ◽  
Cyclic Symmetry ◽  
Specific System ◽  
Strongly Coupled ◽  
Modal Expansion ◽  
Parameter Perturbations ◽  
Bladed Disk Assembly

The effect of small deterministic parameter perturbations on the forced response of nearly periodic structures with cyclic symmetry has been investigated. The general theory developed herein is applicable to any nth order 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 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 quite significantly than would be predicted on the basis of an analysis of the perfectly tuned system. Further, the modal bifurcations lead to uneven vibration amplitudes irrespective of the stiffness of the coupling springs. The variation in blade amplitudes are also found to be strongly dependent on the type of engine order excitation for the same set of mistuning parameter.

Singular perturbation approach to stability of a SIRS epidemic system

2009 ◽  
Vol 10 (5) ◽  
pp. 2688-2699 ◽  
Author(s):  
Zhonghua Zhang ◽  
Yaohong Suo ◽  
Jigen Peng ◽  
Weihua Lin
Keyword(s):  
Singular Perturbation ◽  
Perturbation Approach

Reaction rates when barriers fluctuate: A singular perturbation approach

1998 ◽  
Vol 235 (1-3) ◽  
pp. 11-26 ◽  
Author(s):  
Peter Reimann ◽  
Roland Bartussek ◽  
Peter Hänggi
Keyword(s):  
Singular Perturbation ◽  
Reaction Rates ◽  
Perturbation Approach

scholarly journals Thermal sigmatropic [1,j] shifts in cyclic systems. A perturbation approach and INDO calculations

1977 ◽  
Vol 99 (2) ◽  
pp. 392-397 ◽  
Author(s):  
Jan R. De Dobbelaere ◽  
Jan M. F. Van Dijk ◽  
Jan W. De Haan ◽  
Henk M. Buck
Keyword(s):  
Perturbation Approach ◽  
Indo Calculations ◽  
Cyclic Systems
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