Eigenmode sensitivity of damped sandwich structures

Komlanvi Lampoh; Isabelle Charpentier; Daya El Mostafa

doi:10.1016/j.crme.2014.08.001

Eigenmode sensitivity of damped sandwich structures
[Sensibilité des modes propres de structures sandwich amorties]

Komlanvi Lampoh ¹ ; Isabelle Charpentier ² ; Daya El Mostafa ³

¹ Centre des matériaux, Mines ParisTech, 10, rue Henri-Desbruères, BP 87, 91003 Évry cedex, France
² ICube – Laboratoire des sciences de l'ingénieur, de l'informatique et de l'imagerie, Université de Strasbourg et CNRS, 300, bd Sébastien-Brant, CS 10413, 67412 Illkirch, France
³ Laboratoire d'étude des microstructures et de mécanique des matériaux, UMR 7239, île du Saulcy, 57045 Metz cedex 01, France

Comptes Rendus. Mécanique, Volume 342 (2014) no. 12, pp. 700-705.

est référencé par Erratum to “Eigenmode sensitivity of damped sandwich structures” [C. R. Mecanique 342 (2014) 700–705]

Résumé
Abstract

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.

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.

Reçu le : 2014-06-25
Accepté le : 2014-08-01
Publié le : 2014-08-15

DOI : 10.1016/j.crme.2014.08.001

Keywords: Vibration, Sensitivity, Sandwich structures, Viscoelastic model, Complex nonlinear eigenvalue solver, Automatic differentiation
Mot clés : Vibration, Sensibilité, Structures sandwich, Modèle viscoélastique, Solveur de problèmes aux valeurs propres complexes, Différentiation automatique

Affiliations des auteurs :

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  -

%0 Journal Article
%A Komlanvi Lampoh
%A Isabelle Charpentier
%A Daya El Mostafa
%T Eigenmode sensitivity of damped sandwich structures
%J Comptes Rendus. Mécanique
%D 2014
%P 700-705
%V 342
%N 12
%I Elsevier
%R 10.1016/j.crme.2014.08.001
%G en
%F CRMECA_2014__342_12_700_0

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/

Bibliographie
Cité par

[1] J. Banerjee; C. Cheung; R. Morishima; M. Perera; J. Njuguna 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] E. Daya; M. Potier-Ferry A numerical method for nonlinear eigenvalue problems application to vibrations of viscoelastic structures, Comput. Struct., Volume 79 (2001), pp. 533-541

[3] I. Charpentier; M. Potier-Ferry DIfférentiation automatique de la méthode asymptotique numérique typée: l'approche diamant, C. R. Mecanique, Volume 336 (2008), pp. 336-340

[4] Y. Koutsawa; I. Charpentier; E.M. Daya; M. Cherkaoui 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] B. Cochelin; N. Damil; M. Potier-Ferry Asymptotic numerical methods and padé approximants for non-linear elastic structures, Int. J. Numer. Methods Eng., Volume 37 (1994), pp. 1187-1213

[6] M. Bilasse; I. Charpentier; E.M. Daya; Y. Koutsawa 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] S.H. Chen Eigensolution reanalysis of modified structures using perturbations and Rayleigh quotients, Commun. Numer. Methods Eng., Volume 10 (1994), pp. 111-119

[8] W.B. Bickford 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] U. Kirsch; S.H. Liu Structural reanalysis for general layout modifications, AIAA J., Volume 35 (1997), pp. 382-388

[10] G. Sliva; A. Brezillon; J. Cadou; L. Duigou A study of the eigenvalue sensitivity by homotopy and perturbation methods, J. Comput. Appl. Math., Volume 234 (2010), pp. 2297-2302

[11] A. de Lima; A. Faria; D. Rade Sensitivity analysis of frequency response functions of composite sandwich plates containing viscoelastic layers, Compos. Struct., Volume 92 (2010), pp. 364-376

[12] A. Griewank; A. Walther, SIAM, Philadelphia, PA, USA (2008), p. 438

[13] I. Charpentier On higher-order differentiation in nonlinear mechanics, Optim. Methods Softw., Volume 27 (2012), pp. 221-232

[14] I. Charpentier; B. Cochelin; K. Lampoh Diamanlab – an interactive Taylor-based continuation tool in MATLAB, 2013 | HAL

[15] I. Charpentier Sensitivity of solutions computed through the asymptotic numerical method, C. R. Mecanique, Volume 336 (2008), pp. 788-793

[16] K. Lampoh; I. Charpentier; E.M. Daya 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] E.M. Daya; M. Potier-Ferry A shell finite element for viscoelastically damped sandwich structures, Rev. Eur. Éléments Finis, Volume 11 (2002), pp. 39-56

[18] M. Bilasse; E. Daya; L. Azrar Linear and nonlinear vibrations analysis of viscoelastic sandwich beams, J. Sound Vib., Volume 329 (2010), pp. 4950-4969

[19] S. Ravi; T. Kundra; B. Nakra Single step eigen perturbation method for structural dynamic modification, Mech. Res. Commun., Volume 22 (1995), pp. 363-369

[20] M. Bilasse; L. Azrar; E. Daya Complex modes based numerical analysis of viscoelastic sandwich plates vibrations, Comput. Struct., Volume 89 (2011), pp. 539-555

[21] M.A. Trindade; A. Benjeddou; R. Ohayon Modeling of frequency-dependent viscoelastic materials for active-passive vibration damping, J. Vib. Acoust., Volume 122 (2000), pp. 169-174

[22] I. Elkhaldi; I. Charpentier; E.M. Daya A gradient method for viscoelastic behaviour identification of damped sandwich structures, C. R. Mecanique, Volume 340 (2012), pp. 619-623

[23] P. Guillaume; M. Masmoudi Computation of high order derivatives in optimal shape design, Numer. Math., Volume 67 (1994), pp. 231-250

Cité par Sources :

Commentaires - Politique