Proper Orthogonal Decomposition in Vibration Systems
Proper orthogonal decompostion (POD) has emerged as a prominent tool
in dynamics. It is a modal method, applicable to systems for
which
multiple measurements are simultaneously available, for example
measurements
at several points in a flow field or on an elastic beam. In our
context,
POD is applied to the matrix of multiple measurement locations sampled
through time. POD can be helpful in determining the number of
active
modes in an oscillatory system, and also an optimal representation of
the
form of the modes, which may help in the reduced-order modeling. We
have
tied a fundamental formulation of the proper orthogonal decomposition
to
the normal modes of vibration in both a class of linear and some
special
nonlinear systems. We have also used POD to assist in modal
reduction
of nonlinear oscillators. Recently we are looking at a "complex
orthogonal decomposition" for extracting complex modes for analyzing
wave motions.
Support: National Science Foundation CMS-9624347
(primarily Friction Dynamics),
8/96-7/00;
National Science Foundation CMS-0099603, 9/01-9/04. (Any
opinions, findings, and conclusions or recommendations expressed in
this material are those of the author and do not necessarily reflect
the views of the National Science Foundation.)
Collaborators: Sangbo Han, Kyungnam University, S.
Korea;
Gaetan Kerschen, University de Liege, Belgium.
Publications
- B. F. Feeny and U. Farooq, 2008, "A nonsymmetric state-variable
decomposition for modal analysis," Journal of Sound and Vibration 310
(4-5) 792-800. (preprint)
- B. F. Feeny, 2006, "A method of decomposing wave motions,"
proceedings of the ASME IMECE'06, November 5-10, Chicago, on DVD-ROM.
- G. Kerschen, B.F. Feeny and J.C. Golinval, 2003, "On the
exploitation
of
chaos to build reduced-order models," Computer Methods in Applied
Mechanics
and Engineering 192, 1785-1795. (preprint)
- S. Han and B. F. Feeny, 2003, "Application of proper orthogonal
decomposition
to structural vibration analysis," Mechanical Systems and Signal
Processing.17 (5) 989-1001. (preprint)
- M. S. Riaz and B. F. Feeny, 2003, "Proper orthogonal
decomposition of a
beam sensed with strain gages," Journal of Vibration and Acoustics 125
(1) 129-131. (preprint)
- B. F. Feeny and Y. Liang, 2003, "Interpreting proper orthogonal
modes in
randomly excited vibration systems," Journal of Sound and Vibration 265
(5) 953-966. (preprint)
- B. F. Feeny, 2002, "On proper orthogonal coordinates as
indicators of
modal
activity," Journal of Sound and Vibration 255 (5) 805-817. (preprint)
- B. F. Feeny, 2002, "On the proper orthogonal modes and normal
modes of
continuous vibration systems," Journal of Vibration and Acoustics 124
(1)
157-160. (similar preprint)
- S. Han and B. F. Feeny, 2002, "Enhanced proper orthogonal
decomposition
of homogeneous structures," Journal of Vibration and Control 8
(1)
19-40. (preprint)
- R. Kappagantu and B. F. Feeny, 2000, "Part 1: Dynamical
characterization
of a frictionally excited beam," Nonlinear Dynamics 22 (4) 317-333. (Preprint).
- R. Kappagantu and B. F. Feeny, 2000, "Part 2: Proper orthogonal
modeling
of a frictionally excited beam," Nonlinear Dynamics 23 (1) 1-11. (Preprint).
- R. Kappagantu and B. F. Feeny, 1999, "An 'optimal' modal
reduction of a
system with fritional excitation," Journal of Sound and Vibration
224 (5)
863-877.
- B. F. Feeny and R. Kappagantu, 1998, "On the physical
interpretation of
proper orthogonal modes in vibrations," Journal of Sound and Vibration
211 (4) 607-616. (preprint)
- B. F. Feeny, 1997, "Interpreting proper orthogonal modes in
vibrations,"
Mode Localization and Nonlinear Normal Modes, proceedings of the 1997
Design
Engineering Technical Conferences, Sacramento, CA, September 14-17,
CD-ROM. (similar
preprint)
- M. S. Riaz, 2000, Proper Orthogonal Decomposition of an
Experimental
Beam,
MS Thesis, Michigan State University.
- R. Kappagantu, 1997, An Optimal Modal Reduction for Frictionally
Excited
Systems, PhD thesis, Michigan State University.
