Abstract
Rotor dynamics is the study of vibration behavior in axially symmetric rotating structures which is analyzed to improve the design and decrease the possibility of failure. Excess vibration can cause noise and cyclic stress. There are several phenomena which need to be detected such as centrifugal and gyroscopic effect adding to the complexity in the mathematical procedures in modal analysis. The experimental technique used thus far is called Modal Testing, a well known and widely used technique in research and industry to obtain the Modal and Dynamic response properties of structures. The technique has recently been applied to rotating structures and some research papers been published, however the full implementation of Modal Testing in active structures and the implications are not fully understood and are therefore in need of much further and more in depth investigations. The raw data obtained from experiment was used in finite element (FE) model for comparison, validation purposes. 3-D models result in large number of nodes and elements. This paper demonstrates how to extract a plane 2-D model from the 3-D model that can be used with fewer nodes and elements. The aims is to establish a system identification methodology using the analytical/computational techniques and update the model using experimental techniques already established for passive structures but to active rotating structures, which subsequently help to carry out health monitoring and further design and development
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Abbreviations
- M, C, K,:
-
Mass, damping, and stiffness matrices
- X, f :
-
Displacement, external force vectors
- N :
-
Total number of components
- η r , v r :
-
Components of the modal coordinate and the mode shape vector at the rth mode
- U :
-
Mode shape matrix
- \( \not{{ M}} \), \( \not{{ C}} \) and \(\not{{ K}} \) :
-
Diagonal mass, damping, and stiffness matrices
- μ :
-
Modal force vector
- \( \varphi \) jr the jth :
-
Components of the rth mode shape vector
- x = \( \hat{ x} \) e iωt :
-
Displacement vector of the spatial model
- f j = \( {\hat{ f}_j} \) e iωt :
-
Exciting force
- ω :
-
Excitation frequency
- ω r :
-
Natural frequency of the rth mode (modal parameters)
- ζ r :
-
Damping ratio of the rth mode (modal parameters)
- (FRF) H ij :
-
Ratio of the ith displacement component \( {\hat{x}_i} \) to the jth exciting force component \( {\hat{f}_j} \)
- H ij , r :
-
Peak value of FRF at the rth mode
- Y, Z :
-
Directions at each of the bearing supports
- { },[ ] :
-
Vector, matrix
- T :
-
Matrix transposition
- FRF :
-
Frequency response functions
- FFT :
-
Fast fourier transform
- DOFs :
-
Degree of freedom system
- j :
-
Unit imaginary
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Acknowledgments
The authors are deeply appreciative to the Kingston University London and The Iraqi Ministry of Higher Education, Iraqi cultural attache in London for supporting this research.
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© 2012 The Society for Experimental Mechanics, Inc. 2012
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Al-Khazali, H., Askari, M. (2012). System Identification in Rotating Structures Using Vibration and Modal Analysis. In: Allemang, R., De Clerck, J., Niezrecki, C., Blough, J. (eds) Topics in Modal Analysis I, Volume 5. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-2425-3_46
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DOI: https://doi.org/10.1007/978-1-4614-2425-3_46
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