A new method allowing the determination of normal modes corresponding to the complex ones identified on a structure is proposed. It is based on an appropriation technique applied to forced responses computed from the identified eigensolutions. The set of applied forces is optimized with respect to an appropriation quality criterion. The knowledge of both complex and normal modes allows the full generalized damping matrix to be determined. The complex modes can then be recalculated using the normal modes and the full generalized damping matrix which provides a test of validity by comparison with the original complex modes. Simulated and experimental tests demonstrate the efficiency of this new method.

1.
Fillod, R., 1980, “Contribution a` L’identification des Structures Me´caniques Line´aires,” Thesis, Universite´ de Franche-Comte´, Besanc¸on, France, No. 140.
2.
Zhang, Q., and Lallement, G., 1985, “New Method of Determining the Eigen-solutions of the Associated Conservative Structure from the Identified Eigen-solutions,” IIIrd IMAC, Orlando, pp. 322–328.
3.
Ibrahim
,
S. R.
,
1983
, “
Computations of Normal Modes from Identified Complex Modes
,”
AIAA J.
,
21
, No.
3
, pp.
446
451
.
4.
Zhang, Q., and Lallement, G., 1985, “Simultaneous Determination of Normal Eigenmodes and Generalized Damping Matrix from Complex Eigenmodes,” 2nd International Conference of Aeroelasticity, Aacken.
5.
Niedbal, N., 1984, “Analytical Determination of Real Normal Modes from Measured Complex Modes,” Proceedings of the 25th Structures, Structural Dynamics and Materials Conference, Palm Springs, pp. 292–295.
6.
Imregun, M., and Ewins, D. J., 1993, “Realisation of Complex Mode Shapes,” XIth IMAC, pp. 1303–1309.
7.
Ahamadian, H., Gladwell, G. M. L., and Ismail, F., 1995, “Extracting Real Modes From Complex Measured Modes,” XIIIth IMAC, pp. 507–510.
8.
Koza`nek
,
J.
,
1987
, “
The Qualification Number of a Complex Vector
,”
Mech. Mach. Theory
,
22
, No.
4
, pp.
391
392
.
9.
Balme`s, E., 1994, “New Results on the Identification of Normal Modes from Experimental Complex Modes,” XIIth IMAC, pp. 1576–1582.
10.
Wei, M. L., Allemang, R. J., and Brown, D. L., 1987, “Real-Normalization of Measured Complex Modes,” Vth IMAC, pp. 708–712.
11.
Fillod
,
R.
, and
Piranda
,
J.
,
1978
, “
Research Method of the Eigenvalues and Generalized Elements of a Linear Mechanical Structure
,”
Shock Vibr. Bull.
,
48
, No.
3
, pp.
5
12
.
12.
Ratsifandrihana, L., 1995, “Ame´lioration des Proce´dures d’Identification Modale des Structures par Appropriation Automatique et Utilisation de Forces Non-Contro^le´es,” Ph.D. thesis, Universite´ de Franche-Comte´, Besanc¸on, France, No. 456.1995.
You do not currently have access to this content.