A method for updating joint parameters in medium-frequency vibrations
DOI:
https://doi.org/10.13052/REMN.17.713-723Keywords:
medium frequency, joints, damping, updating, VTCR,, inverse problem, domain decomposition methodsAbstract
Joints between substructures play a significant role in the vibrational behavior of complex structures because they govern energy flow and most of the dissipative phenomena. In order to identify joint models, this paper proposes a robust updating method which was initially based on studies of the error in constitutive relation in relation to finite element model updating. Here, it is redesigned in order to focus on joint models in medium-frequency problems. In order to do that, we use an alternative numerical approach called the Variational Theory of Complex Rays (VTCR). After introducing the new formulation, the paper analyzes the effectiveness of the approach in identifying a joint’s stiffness and damping.
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References
Bonnet M., Constantinescu A., “ Inverse problems in elasticity”, Inverse Problems, vol. 21,
p. R1-R50, 2005.
Deraemaeker A., Sur la maîtrise des modèles en dynamique des structures à partir de résultats
d’essais, PhD thesis, Université Paris VI - ENS Cachan, 2001.
Dorival O., Rouch P., Allix O., “ A substructured version of the variational theory of complex
rays dedicated to the calculation of assemblies with dissipative joints in the mediumfrequency
range”, Engineering Computations, vol. 23, n° 7, p. 729-748, 2006.
Dorival O., Rouch P., Allix O., “ A substructured Trefftz method for updating joint models in
the medium-frequency range”, Computational Mechanics, vol. 42, p. 381-394, 2008.
Farhat C., Harari I., Hetmaniuk U., “ A discontinuous Galerkin method with Lagrange multipliers
for the solution of Helmholtz problems in the mid-frequency regime”, Comput. Methods
Appl. Mech. Engrg., vol. 192, p. 1389-1419, 2003.
Ihlenburg F., Bab˘uska I., “ Finite element solution of the Helmholtz equation with high wave
number. Part II: The h-p-version of the FEM”, Siam J. of Numer. Anal., vol. 34, n° 1, p. 315-
, 1997.
Ladevèze P., Chouaki A., “ Application of a posteriori error estimation for structural model
updating”, Inverse Problems, vol. 15, p. 49-58, 1999.
Ladevèze P., Leguillon D., “ Error estimate procedure in the finite element method and application”,
SIAM J. Numer. Anal., vol. 20, n° 3, p. 485-509, 1983.
Ladevèze P., Rouch P., Riou H., Bohineust X., “ Analysis of medium-frequency vibrations in a
frequency range”, Jnl of Comp. Acoustic, vol. 11, n° 2, p. 255-283, 2003.
Lyon R. H., Statistical Energy Analysis of dynamical systems: theory and applications, MIT
Press, Cambridge, 1975.
Maxit L., Guyader J.-L., “ Estimation of SEA coupling loss factors using a dual formulation
and FEMmodal information, Part I: theory”, Journal of Sound and Vibration, vol. 239, n° 5,
p. 907-930, 2001.
Mottershead J., Friswell M., “ Model updating in structural dynamics: a survey”, Journal of
Sound and Vibration, vol. 167, n° 2, p. 347-375, 1993.
Strouboulis T., Babuska I., Hidajat R., “ The Generalized Finite Element Method for Helmholtz
equation: theory, computations and open problems”, Comput. Meth. Appl. Mech. Engrg.,
vol. 195, p. 4711-4731, 2006.
Wang J., Liou C., “ Experimental identification of mechanical joint parameters”, Journal of
Vibration and Acoustics, vol. 113, p. 28-36, 1991. Transaction of the ASME.
