The modeling of the linear free vibration of a sandwich structure including viscoelastic layers yields a complex nonlinear eigenvalue problem. In this paper, the sensitivity of eigensolutions is computed using a homotopy-based asymptotic numerical method, then a first-order automatic differentiation. The generality of the proposed method enables us to consider any analytical frequency-dependent viscoelastic law in the modeling and the sensitivity computation. Its application potential is demonstrated by computing the sensitivity of eigenmodes, eigenfrequencies and modal loss factors of sandwich beams and plates to various perturbations.
La modélisation des vibrations linéaires libres d'une structure sandwich comportant des couches visco-élastiques conduit à un problème aux valeurs propres non linéaires complexes. Dans cet article, la sensibilité des solutions propres est calculée en utilisant une méthode asymptotique numérique, puis une différentiation automatique d'ordre un. La généralité de la méthode proposée permet de considérer toute loi visco-élastique analytique avec dépendance en fréquence dans la modélisation et le calcul de sensibilité. Son potentiel applicatif est démontré en calculant la sensibilité des valeurs et vecteurs propres, et des facteurs de perte modaux de poutres et plaques sandwich à différentes perturbations.
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Mots-clés : Vibration, Sensibilité, Structures sandwich, Modèle viscoélastique, Solveur de problèmes aux valeurs propres complexes, Différentiation automatique
Komlanvi Lampoh 1; Isabelle Charpentier 2; Daya El Mostafa 3
@article{CRMECA_2014__342_12_700_0,
author = {Komlanvi Lampoh and Isabelle Charpentier and Daya El Mostafa},
title = {Eigenmode sensitivity of damped sandwich structures},
journal = {Comptes Rendus. M\'ecanique},
pages = {700--705},
publisher = {Elsevier},
volume = {342},
number = {12},
year = {2014},
doi = {10.1016/j.crme.2014.08.001},
language = {en},
}
TY - JOUR AU - Komlanvi Lampoh AU - Isabelle Charpentier AU - Daya El Mostafa TI - Eigenmode sensitivity of damped sandwich structures JO - Comptes Rendus. Mécanique PY - 2014 SP - 700 EP - 705 VL - 342 IS - 12 PB - Elsevier DO - 10.1016/j.crme.2014.08.001 LA - en ID - CRMECA_2014__342_12_700_0 ER -
Komlanvi Lampoh; Isabelle Charpentier; Daya El Mostafa. Eigenmode sensitivity of damped sandwich structures. Comptes Rendus. Mécanique, Volume 342 (2014) no. 12, pp. 700-705. doi : 10.1016/j.crme.2014.08.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2014.08.001/
[1] Free vibration of a three-layered sandwich beam using the dynamic stiffness method and experiment, Int. J. Solids Struct., Volume 44 (2007), pp. 7543-7563
[2] A numerical method for nonlinear eigenvalue problems application to vibrations of viscoelastic structures, Comput. Struct., Volume 79 (2001), pp. 533-541
[3] DIfférentiation automatique de la méthode asymptotique numérique typée: l'approche diamant, C. R. Mecanique, Volume 336 (2008), pp. 336-340
[4] A generic approach for the solution of nonlinear residual equations. Part I: The Diamant toolbox, Comput. Methods Appl. Math., Volume 198 (2008), pp. 572-577
[5] Asymptotic numerical methods and padé approximants for non-linear elastic structures, Int. J. Numer. Methods Eng., Volume 37 (1994), pp. 1187-1213
[6] A generic approach for the solution of nonlinear residual equations. Part II: Homotopy and complex nonlinear eigenvalue method, Comput. Methods Appl. Math., Volume 198 (2009), pp. 3999-4004
[7] Eigensolution reanalysis of modified structures using perturbations and Rayleigh quotients, Commun. Numer. Methods Eng., Volume 10 (1994), pp. 111-119
[8] An improved computational technique for pertubations of the generalized symmetric linear algebraic eigenvalue problem, Int. J. Numer. Methods Eng., Volume 24 (1987), pp. 529-541
[9] Structural reanalysis for general layout modifications, AIAA J., Volume 35 (1997), pp. 382-388
[10] A study of the eigenvalue sensitivity by homotopy and perturbation methods, J. Comput. Appl. Math., Volume 234 (2010), pp. 2297-2302
[11] Sensitivity analysis of frequency response functions of composite sandwich plates containing viscoelastic layers, Compos. Struct., Volume 92 (2010), pp. 364-376
[12] , SIAM, Philadelphia, PA, USA (2008), p. 438
[13] On higher-order differentiation in nonlinear mechanics, Optim. Methods Softw., Volume 27 (2012), pp. 221-232
[14] Diamanlab – an interactive Taylor-based continuation tool in MATLAB, 2013 | HAL
[15] Sensitivity of solutions computed through the asymptotic numerical method, C. R. Mecanique, Volume 336 (2008), pp. 788-793
[16] A generic approach for the solution of nonlinear residual equations. Part III: Sensitivity computations, Comput. Methods Appl. Math., Volume 200 (2011), pp. 2983-2990
[17] A shell finite element for viscoelastically damped sandwich structures, Rev. Eur. Éléments Finis, Volume 11 (2002), pp. 39-56
[18] Linear and nonlinear vibrations analysis of viscoelastic sandwich beams, J. Sound Vib., Volume 329 (2010), pp. 4950-4969
[19] Single step eigen perturbation method for structural dynamic modification, Mech. Res. Commun., Volume 22 (1995), pp. 363-369
[20] Complex modes based numerical analysis of viscoelastic sandwich plates vibrations, Comput. Struct., Volume 89 (2011), pp. 539-555
[21] Modeling of frequency-dependent viscoelastic materials for active-passive vibration damping, J. Vib. Acoust., Volume 122 (2000), pp. 169-174
[22] A gradient method for viscoelastic behaviour identification of damped sandwich structures, C. R. Mecanique, Volume 340 (2012), pp. 619-623
[23] Computation of high order derivatives in optimal shape design, Numer. Math., Volume 67 (1994), pp. 231-250
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