Numerical comparison of reduced order models for non-linear vibrations of damped plates

References

• Abdoun , F. , Azrar , L. , Daya , E.M. and Potier-Ferry , M. 2009 . Forced harmonic response of viscoelastic structures by an asymptotic numerical method . Computers & Structures , 87 : 91 – 100 .
   Google Scholar
• Amabili , M. , Sarkar , A. and Paıdoussis , M.P. 2003 . Reduced-order models for nonlinear vibrations of cylindrical shells via the proper orthogonal decomposition method . Journal of Fluids and Structures , 18 : 227 – 250 .
   Google Scholar
• Antoulas , A.C. and Sorensen , D.C. 2001 . Approximation of large-scale dynamical systems: An overview . International Journal of Applied Mathematics and Computer Science , 11 ( 5 ) : 1093 – 1121 .
   Google Scholar
• Batoz , J.-L. and Dhatt , G. 1992 . Modeling of structures by the finite element method (Vol. 3: shells) , Paris : Hermès .
   Google Scholar
• Boumediene , F. , Duigou , L. , Boutyour , E.H. , Miloudi , A. and Cadou , J.M. 2011 . Nonlinear forced vibration of damped plates coupling asymptotic numerical method and reduction models . Computational Mechanics , 47 ( 4 ) : 359 – 377 .
   Google Scholar
• Boumediene , F. , Miloudi , A. , Cadou , J.M. , Duigou , L. and Boutyour , E.H. 2009 . Nonlinear forced vibration of damped plates by an asymptotic numerical method . Computers & Structures , 87 : 1508 – 1515 .
   Google Scholar
• Brezillon , A. , Girault , G. and Cadou , J.M. 2010 . A numerical algorithm coupling a bifurcating indicator and a direct method for the computation of Hopf bifurcation points in fluid mechanics . Computers & Fluids , 39 ( 7 ) : 1226 – 1240 .
   Google Scholar
• Cadou , J.M. , Cochelin , B. , Damil , N. and Potier-Ferry , M. 2001 . Asymptotic numerical method for stationary Navier-Stokes equations and with Petrov-Galerkin formulation . International Journal of Numerical Methods in Engineering , 50 : 825 – 845 .
   Google Scholar
• Cadou , J.M. and Potier-Ferry , M. 2010 . A solver combining reduced basis and convergence acceleration with applications in non-linear elasticity . International Journal for Numerical Methods in Biomedical , 26 : 1604 – 1617 .
   Google Scholar
• Cochelin , B. , Damil , N. and Potier-Ferry , M. 1994 . Asymptotic numerical methods and Padé approximants for non-linear elastic structures . International Journal for Numerical methods in Engineering , 37 : 1187 – 1213 .
   Google Scholar
• Cochelin , B. and Vergez , C. 2009 . A high order purely frequency-based harmonic balance formulation for continuation of periodic solutions . Journal of Sound and Vibration , 324 : 243 – 262 .
   Google Scholar
• Daridon , L. , Wattrisse , B. , Chrysochoos , A. and Potier-Ferry , M. 2011 . Solving fracture problems using an asymptotic numerical method . Computers & Structures , 89 ( 5–6 ) : 476 – 484 .
   Google Scholar
• Elhage-Hussein , A. , Potier-Ferry , M. and Damil , N. 2000 . A numerical continuation method based on Padé approximants . International Journal of Solids and Structures , 37 : 6981 – 7001 .
   Google Scholar
• Goncalves , P.B. , Silva , F.M.A. and Del Prado , Z.J.G.N. 2008 . Low-dimensional models for the nonlinear vibration analysis of cylindrical shells based on a perturbation procedure and proper orthogonal decomposition . Journal of Sound and Vibration , 315 : 641 – 663 .
   Google Scholar
• Holmes , P. , Lumley , J.L. and Berkooz , G. 1996 . Turbulence, coherent structures, dynamical systems and symmetry , Cambridge : Cambridge University Press .
   Google Scholar
• LaBryer , A. and Attar , P.J. 2010 . A harmonic balance approach for large-scale problems in nonlinear structural dynamics . Computers & Structures , 88 : 1002 – 1014 .
   Google Scholar
• Lall , S. , Krysl , P. and Marsden , J.E. 2003 . Structure-preserving model reduction for mechanical systems . Physica D: Nonlinear Phenomena , 184 : 304 – 318 .
   Google Scholar
• Médale , M. and Cochelin , B. 2009 . A parallel computer implementation of the asymptotic numerical method to study thermal convection instabilities . Journal of Computational Physics , 228 ( 22 ) : 8249 – 8262 .
   Google Scholar
• Mickens R.E. (2010). Truly nonlinear oscillations. Harmonic Balance, parameter expansions, iteration, and averaging methods. USA: World Scientific Publishing Co. Pte. Ltd.
   Google Scholar
• Mottaqui , H. , Braikat , B. and Damil , N. 2010 . Discussion about parametrization in the asymptotic numerical method: Appmlication to nonlinear elastic shell . Computer Methods in Applied Mechanics and Engineering , 199 ( 25–28 ) : 1701 – 1709 .
   Google Scholar
• Potier-Ferry , M. , Damil , N. , Braikat , B. , Descamps , J. , Cadou , J.-M. , Lei Cao , H. and Elhage Hussein , A. 1997 . Treatment of strong non-linearities by the asymptotic numerical method . Comptes Rendus de l’Académie des Sciences - Series II , b324 ( 3 ) : 171 – 177 .
   Google Scholar
• Wriggers , P. 2008 . Nonlinear finite element methods , Berlin : Springer-Verlag .
   Google Scholar
• Yvonnet , J. and He , Q.C. 2007 . The reduced model multiscale method (R3M) for the non-linear homogenization of hyperelastic media at finite strains . Journal of Computational Physics , 223 : 341 – 368 .
   Google Scholar