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Research Papers: Gas Turbines: Structures and Dynamics

Nonparametric Stochastic Modeling of Uncertainty in Rotordynamics—Part I: Formulation

[+] Author and Article Information
Raghavendra Murthy, Marc P. Mignolet

Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ 85287-6106

Aly El-Shafei

Department of Mechanical Design and Production, Cairo University, Giza 12316, Egypt

J. Eng. Gas Turbines Power 132(9), 092501 (Jun 07, 2010) (7 pages) doi:10.1115/1.3204645 History: Received March 24, 2009; Revised March 25, 2009; Published June 07, 2010; Online June 07, 2010

A systematic and rational approach is presented for the consideration of uncertainty in rotordynamics systems, i.e., in rotor mass and gyroscopic matrices, stiffness matrix, and bearing coefficients. The approach is based on the nonparametric stochastic modeling technique, which permits the consideration of both data and modeling uncertainty. The former is induced by a lack of exact knowledge of properties such as density, Young’s modulus, etc. The latter occurs in the generation of the computational model from the physical structure as some of its features are invariably ignored, e.g., small anisotropies, or approximately represented, e.g., detailed meshing of gears. The nonparametric stochastic modeling approach, which is briefly reviewed first, introduces uncertainty in reduced order models through the randomization of their system matrices (e.g., stiffness, mass, and damping matrices of nonrotating structural dynamic systems). Here, this methodology is extended to permit the consideration of uncertainty in symmetric and asymmetric rotor dynamic systems. More specifically, uncertainties on the rotor stiffness (stiffness matrix) and/or mass properties (mass and gyroscopic matrices) are first introduced that maintain the symmetry of the rotor. The generalization of these concepts to uncertainty in the bearing coefficients is achieved next. Finally, the consideration of uncertainty in asymmetric rotors is described in detail.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

Structure of the random H͇ matrices (figures for n=8, i=2, and λ=1 and 10)

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