To determine the natural frequencies and damping ratios of composite laminated plates, we present an efficient modal parameter estimation technique by developing a residual spectrum based structural dynamic system reconstruction. The modal parameters can be estimated from poles and residues of the system transfer functions derived from the state space system matrices. However, for modal parameter estimation of multivariable and higher order structural systems over broad frequency bands, this noniterative algorithm gives high accuracy in determining the natural frequencies and damping ratios. It is numerically well-behaved unlike iterative frequency-response-function (FRF) curve-fitting methods. We also discuss necessary conditions for convergence in Hankel norm and the error bounds of the approximated transfer function for the IDFT-based reconstruction system. From vibration tests on cross-ply and angle-ply composite laminates, the natural frequencies and damping ratios can be identified from the eigenvalues of the structural dynamic system matrix derived by the reconstruction method from the experimental frequency response functions. These results are compared with those of finite-element analysis and single-degree-of-freedom curve-fitting.

Issue Section:
Technical Papers
Keywords:
parameter estimation, flexible structures, transfer functions, sampled data systems, eigenvalues and eigenfunctions, laminates, convergence, vibrations
Topics:
Algorithms, Composite materials, Damping, Errors, Frequency response, Laminates, Structural dynamics, Transfer functions, Approximation, Eigenvalues, Parameter estimation, Plates (structures), Vibration tests, Curve fitting
1.
SDRC, 1994, IDEAS Test, User Guide Vol II.
2.
Ho
,
B.
, and
Kalman
,
R.
,
1966
, “
Efficient Construction of Linear State Variable Models From Input/Output Functions
,”
Regelungstechnik
,
14
, pp.
545
–
548
.
3.
Juang
,
J. N.
, and
Pappa
,
R. S.
,
1985
, “
An Eigensystem Realization Algorithm for Modal Parameter Identification and Model Reduction
,”
J. Guid. Control Dyn.
,
8
(
5
), pp.
583
–
592
.
4.
Juang
,
J. N.
, and
Pappa
,
R. S.
,
1985
, “
An Eigensystem Realization Algorithm Using Data Correlation (ERA/DC) for Modal Parameter Identification
,”
J. Control Theory Adv. Technol.
,
4
(
1
), pp.
5
–
14
.
5.
Liu
,
K.
, and
Skelton
,
R. E.
,
1993
, “
Q-Markov Covariance Equivalent Realization and its Application to Flexible Structural Identification
,”
J. Guid. Control Dyn.
,
16
(
2
), pp.
308
–
319
.
6.
Liu
,
K.
, and
Miller
,
D. W.
,
1995
, “
Time Domain State Space Identification of Structural Systems
,”
ASME J. Dyn. Syst., Meas., Control
,
117
, pp.
608
–
618
.
7.
Van Overschee, P., and De Moor, B., 1996, Subspace Identification for Linear Systems, Theory-Implementation-Application, Kluwer Academic Publishers, Dordrecht.
8.
Chen, C. W., Juang, J. N., and Lee, G., 1993, “Frequency Domain State-Space System Identification,” Proceedings of 1993 American Control Conference, San Francisco, CA.
9.
Liu
,
K.
,
Jacques
,
R. N.
, and
Miller
,
D. W.
,
1996
, “
Frequency Domain Structural System Identification by Observability Rang Space Extraction
,”
ASME J. Dyn. Syst., Meas., Control
,
118
, pp.
211
–
220
.
10.
Reddy
,
J. N.
,
1979
, “
Free Vibration of Antisymmetric, Angle-Ply Laminated Plates Including Transverse Shear Deformation by the Finite Element Method
,”
J. Sound Vib.
,
66
(
4
), pp.
565
–
576
.
11.
Lin
,
D. X.
,
Ni
,
R. G.
, and
Adams
,
R. D.
,
1984
, “
Prediction and Measurement of the Vibrational Damping Parameters of Carbon and Glass Fibre-Reinforced Plastics Plates
,”
J. Compos. Mater.
,
18
, pp.
132
–
152
.
12.
Batoz
,
J.
, and
Tahar
,
M. B.
,
1982
, “
Evaluation of a New Quadrilateral Thin Plate Bending Elements
,”
Int. J. Numer. Methods Eng.
,
18
, pp.
1655
–
1677
.
13.
Ljung, L., 1987, System Identification: Theory for the User, Prentice-Hall, Englewood Cliffs, N.J.
14.
Lancaster, P., and Tismenetsky, M., 1985, The Theory of Matrices, 2nd ed., Academic, New York.
15.
Wheeden, R. L., and Zygmund, A., 1977, Measure and Integral: An Introduction to Real Analysis, Marcel-Dekker, New York.
16.
Kamen
,
E. W.
,
Khargoneker
,
P. P.
, and
Tannenbaum
,
A.
,
1985
, “
Stabilization of Time-Delay System With Finite-Dimensional Compensator
,”
IEEE, A.C.
,
30
, pp.
75
–
78
.
17.
Rudin, W., 1987, Real and Complex Analysis, 3rd ed., McGraw-Hill, Marcel–Dekker, N.Y.
18.
Partington, J. R., 1988, An Introduction to Hankel Operators, Cambridge University Press.
19.
Zhou, K., Doyle, J. C., and Glover, K., 1996, Robust and Optimal Control, Prentice-Hall, Englewood Cliffs, N.J.
20.
Glover
,
K.
,
1984
, “
All Optimal Hankel-Norm Approximation of Linear Multivariable System and Their L∞-Error Bounds
,”
Int. J. Contr.
,
39
, pp.
1115
–
1193
.
21.
Pandit, S. M., 1991, Modal and Spectrum Analysis: Data Dependent Systems in State Space, Wiley-Interscience Publication, New York.
Copyright © 2003
 by ASME
You do not currently have access to this content.