This paper focuses on developing a full-state observer that can be used to obtain unmeasurable reaction forces in a flexible structure. In the context of modal truncation of a distributed parameter system, accurate representation of reaction forces is discussed and is shown to require a more comprehensive model than for displacement representation. This fact, coupled with the difficulty in directly measuring reaction forces in many applications points to the need for accurate estimation of ferees with reduced-order models. The residual flexibility, a term from past literature, is used to recapture some of the lost force information in a truncated model. This paper presents numerical and experimental results of a study where the residual flexibility is used in conjunction with a Kalman filter so that accurate force information may be obtained from a small set of displacement measurements with a reduced-order model. The motivation for this paper is to be able to obtain accurate information about dynamic bearing loads in a rotating machine for diagnostic and control purposes.

1.
Garwronski
W.
, and
Natake
H.
,
1986
, “
On Balancing Linear Symmetric Systems
,”
International Journal of Systems Science
, Vol.
17
, pp.
1509
1519
.
2.
Guyan
R.
,
1965
, “
Reduction of Stiffness and Mass Matrices
,”
AIAA Journal
, Vol.
3
, p.
380
380
.
3.
Hanseen
O. E.
, and
Bell
K.
,
1979
, “
On the Accuracy of Mode Superposition Analysis in Structural Dynamics
,”
Earthquake Engineering and Structural Dynamics
, Vol.
7
, pp.
405
411
.
4.
Kim, J. H., Clark, W. W., and Marangoni, R. D., 1993, “Feedback Techniques for Minimizing Bearing Loads in Rotating Machinery,” Second Conference on Recent Advances in Active Control of Sound and Vibration, R. A. Burdisso, ed., Technomics Publishing Co., Inc., Lancaster, PA, pp. 885–896.
5.
Kwakernaak, H., and Sivan, R., 1972, Linear Optimal Control Systems, Wiley-Interscience, New York.
6.
Lewis, D. E., and Allaire, P. E., 1987, “Rotor to Base Control of Rotation Machinery to Minimize Transmitted Force,” Structural Control, H. H. E., Leipholz, ed., Matimas Nijhoff Publishers, Dordrecht, The Netherlands, pp. 408–425.
7.
Maddox, N. R., 1975, “On the Number of Modes Necessary for Accurate Response and Resulting Forces in Dynamic Analysis,” ASME Journal of Applied Mechanics, pp. 516–517.
8.
Meirovitch, L., 1986, Elements of Vibration Analysis, McGraw-Hill, New York, NY.
9.
Meirovitch
L.
, and
Oz
H.
,
1980
, “
Modal-Space Control of Distributed Gyroscopic Systems
,”
Journal of Guidance and Control
, Vol.
3
, No.
2
, pp.
140
150
.
10.
Meirovitch
L.
, and
Silverberg
L.
,
1985
, “
Control of Non-Self-Adjoint Distributed Parameter Systems
,”
Journal of Optimization Theory and Applications
, Vol.
47
, No.
1
, pp.
77
90
.
11.
Nelson, H., and McVaugh, J., 1976, “The Dynamics of Rotor-Bearing Systems Using Finite Elements,” ASME Journal of Engineering for Industry, pp. 593–600.
12.
Petyt, M., 1990, Introduction to Finite Element Vibration Analysis, Cambridge Univ. Press, Boston, MA.
13.
Scribner, K. B., 1990, “Active Narrow Band Vibration Isolation of Machinery Noise from Resonant Substructures,” M.S. Thesis, MIT.
14.
Sievers, L., and Von Flotow, A. H., 1990, “Comparison and Extensions of Control Methods for Narrowband Disturbance Rejection,” Proceedings of the ASME Winter Annual Meeting, Dallas, TX.
15.
Stengel, R. F., 1986, Stochastic Optimal Control, John Wiley and Sons, New York, NY.
16.
Yae
K.
, and
Inman
D.
,
1993
, “
Control-Oriented Order Reduction of Finite Element Model
,”
ASME Journal of Dynamic Systems, Measurement, and Control
, Vol.
115
, pp.
708
711
.
This content is only available via PDF.
You do not currently have access to this content.