Adjoint systems and the theory of invariants

Adjoint Systems and the Theory of Invariants

Algebraic Surfaces - Classics in Mathematics ◽

10.1007/978-3-642-61991-5_3 ◽

1995 ◽

pp. 51-74

Author(s):

David Mumford

Keyword(s):

Adjoint Systems ◽

Theory Of Invariants

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Inverse sensitivity method to self-adjoint systems with repeated eigenvalues

AIAA Journal ◽

10.2514/3.14266 ◽

1999 ◽

Vol 37 ◽

pp. 933-938

Author(s):

H. W. Song ◽

L. F. Chen ◽

W. L. Wang

Keyword(s):

Adjoint Systems ◽

Repeated Eigenvalues ◽

Sensitivity Method

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A System Identification Method for Excitation-Frequency Dependent Rotordynamic Coefficients

Volume 7: Structures and Dynamics, Parts A and B ◽

10.1115/gt2012-69311 ◽

2012 ◽

Author(s):

Timothy W. Dimond ◽

Amir A. Younan ◽

Paul Allaire

Keyword(s):

System Identification ◽

Measurement Uncertainty ◽

Excitation Frequency ◽

Frequency Dependent ◽

Rotordynamic Coefficients ◽

Adjoint Systems ◽

Dynamic Coefficients ◽

Backward Whirl ◽

Identification Technique ◽

Damped Systems

Experimental identification of rotordynamic systems presents unique challenges. Gyroscopics, generally damped systems, and non-self-adjoint systems due to fluid structure interaction forces mean that symmetry cannot be used to reduce the number of parameters to be identified. Rotordynamic system experimental measurements are often noisy, which complicates comparisons with theory. When linearized, the resulting dynamic coefficients are also often a function of excitation frequency, as distinct from operating speed. In this paper, a frequency domain system identification technique is presented that addresses these issues for rigid-rotor test rigs. The method employs power spectral density functions and forward and backward whirl orbits to obtain the excitation frequency dependent effective stiffness and damping. The method is highly suited for use with experiments that employ active magnetic exciters that can perturb the rotor in the forward and backward whirl directions. Simulation examples are provided for excitation-frequency reduced tilting pad bearing dynamic coefficients. In the simulations, 20 and 50 percent Gaussian output noise was considered. Based on ensemble averages of the coefficient estimates, the 95 percent confidence intervals due to noise effects were within 1.2% of the identified value. The method is suitable for identification of linear dynamic coefficients for rotordynamic system components referenced to shaft motion. The method can be used to reduce the effect of noise on measurement uncertainty. The statistical framework can also be used to make decisions about experimental run times and acceptable levels of measurement uncertainty. The data obtained from such an experimental design can be used to verify component models and give rotordynamicists greater confidence in the design of turbomachinery.

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