메뉴 건너뛰기




Volumn 49, Issue 8, 2014, Pages 1901-1916

An effective finite-element-based method for the computation of nonlinear normal modes of nonconservative systems

Author keywords

Finite element method; Invariant manifolds; Modal analysis; Nonconservative systems; Nonlinear normal modes

Indexed keywords

FINITE ELEMENT METHOD; GALERKIN METHODS; MODAL ANALYSIS; PHASE SPACE METHODS;

EID: 84905109742     PISSN: 00256455     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11012-014-9875-3     Document Type: Article
Times cited : (36)

References (41)
  • 1
    • 33645049419 scopus 로고
    • On nonlinear vibrations of systems with many degrees of freedom
    • 10.1016/S0065-2156(08)70008-5
    • Rosenberg RM (1966) On nonlinear vibrations of systems with many degrees of freedom. Adv Appl Mech 9:155-242
    • (1966) Adv Appl Mech , vol.9 , pp. 155-242
    • Rosenberg, R.M.1
  • 3
    • 0027911991 scopus 로고
    • Normal modes for non-linear vibratory systems
    • 10.1006/jsvi.1993.1198 1231018
    • Shaw SW, Pierre C (1993) Normal modes for non-linear vibratory systems. J Sound Vib 164:40
    • (1993) J Sound Vib , vol.164 , pp. 40
    • Shaw, S.W.1    Pierre, C.2
  • 4
    • 0030780655 scopus 로고    scopus 로고
    • Non-linear normal modes (NNMs) and their applications in vibration theory: An overview
    • 1997MSSP.11.3V 10.1006/mssp.1996.9999 1436378
    • Vakakis AF (1997) Non-linear normal modes (NNMs) and their applications in vibration theory: an overview. Mech Syst Signal Process 11(1):3-22
    • (1997) Mech Syst Signal Process , vol.11 , Issue.1 , pp. 3-22
    • Vakakis, A.F.1
  • 5
    • 0026223029 scopus 로고
    • Analysis of non-linear dynamical systems by the normal form theory
    • 1991JSV.149.429J 10.1016/0022-460X(91)90446-Q
    • Jezequel L, Lamarque CH (1991) Analysis of non-linear dynamical systems by the normal form theory. J Sound Vib 149(3):429-459
    • (1991) J Sound Vib , vol.149 , Issue.3 , pp. 429-459
    • Jezequel, L.1    Lamarque, C.H.2
  • 6
    • 3943076520 scopus 로고    scopus 로고
    • Nonlinear normal modes of structural systems via asymptotic approach
    • 10.1016/j.ijsolstr.2004.04.029 1073.74032
    • Lacarbonara W, Camillacci R (2004) Nonlinear normal modes of structural systems via asymptotic approach. Int J Solids Struct 41(20):5565-5594
    • (2004) Int J Solids Struct , vol.41 , Issue.20 , pp. 5565-5594
    • Lacarbonara, W.1    Camillacci, R.2
  • 7
    • 4644266024 scopus 로고    scopus 로고
    • Bifurcations of nonlinear normal modes of linear oscillator with strongly nonlinear damped attachment
    • 10.1023/B:NODY.0000042911.49430.25 1081.70012 2098826
    • Gendelman OV (2004) Bifurcations of nonlinear normal modes of linear oscillator with strongly nonlinear damped attachment. Nonlinear Dyn 37(2):115-128
    • (2004) Nonlinear Dyn , vol.37 , Issue.2 , pp. 115-128
    • Gendelman, O.V.1
  • 8
    • 34249797583 scopus 로고    scopus 로고
    • Dimension reduction of homoclinic orbits of buckled beams via the non-linear normal modes technique
    • 10.1016/j.ijnonlinmec.2007.02.004 1200.74091
    • Lenci S, Rega G (2007) Dimension reduction of homoclinic orbits of buckled beams via the non-linear normal modes technique. Int J Non-linear Mech 42(3):515-528
    • (2007) Int J Non-linear Mech , vol.42 , Issue.3 , pp. 515-528
    • Lenci, S.1    Rega, G.2
  • 9
    • 77956614808 scopus 로고    scopus 로고
    • Nonlinear normal modes of a self-excited system driven by parametric and external excitations
    • 10.1007/s11071-010-9679-5 1204.70027 2718352
    • Warminski J (2010) Nonlinear normal modes of a self-excited system driven by parametric and external excitations. Nonlinear Dyn 61(4):677-689
    • (2010) Nonlinear Dyn , vol.61 , Issue.4 , pp. 677-689
    • Warminski, J.1
  • 10
    • 18844436998 scopus 로고    scopus 로고
    • Complicated dynamics of a linear oscillator with a light, essentially nonlinear attachment
    • 2005PhyD.204.41L 10.1016/j.physd.2005.03.014 1179.70013 2147471
    • Lee YS, Kerschen G, Vakakis AF, Panagopoulos P, Bergman L, McFarland DM (2005) Complicated dynamics of a linear oscillator with a light, essentially nonlinear attachment. Physica D 204(1-2):41-69
    • (2005) Physica D , vol.204 , Issue.1-2 , pp. 41-69
    • Lee, Y.S.1    Kerschen, G.2    Vakakis, A.F.3    Panagopoulos, P.4    Bergman, L.5    McFarland, D.M.6
  • 11
    • 53849093038 scopus 로고    scopus 로고
    • Nonlinear normal modes, part I: A useful framework for the structural dynamicist
    • 2009MSSP.23.170K 10.1016/j.ymssp.2008.04.002
    • Kerschen G, Peeters M, Golinval JC, Vakakis AF (2009) Nonlinear normal modes, part I: A useful framework for the structural dynamicist. Mech Syst Signal Process 23(1):170-194
    • (2009) Mech Syst Signal Process , vol.23 , Issue.1 , pp. 170-194
    • Kerschen, G.1    Peeters, M.2    Golinval, J.C.3    Vakakis, A.F.4
  • 12
    • 33746882845 scopus 로고    scopus 로고
    • Two methods for the computation of nonlinear modes of vibrating systems at large amplitudes
    • 10.1016/j.compstruc.2006.01.011 2248882
    • Arquier R, Bellizzi S, Bouc R, Cochelin B (2006) Two methods for the computation of nonlinear modes of vibrating systems at large amplitudes. Comput Struct 84(24-25):1565-1576
    • (2006) Computers & Structures , vol.84 , Issue.24-25 , pp. 1565-1576
    • Arquier, R.1    Bellizzi, S.2    Bouc, R.3    Cochelin, B.4
  • 13
    • 53849083425 scopus 로고    scopus 로고
    • Nonlinear normal modes, part II: Toward a practical computation using numerical continuation techniques
    • 2009MSSP.23.195P 10.1016/j.ymssp.2008.04.003
    • Peeters M, Viguié R, Sérandour G, Kerschen G, Golinval JC (2009) Nonlinear normal modes, part II: Toward a practical computation using numerical continuation techniques. Mech Syst Signal Process 23(1):195-216
    • (2009) Mech Syst Signal Process , vol.23 , Issue.1 , pp. 195-216
    • Peeters, M.1    Viguié, R.2    Sérandour, G.3    Kerschen, G.4    Golinval, J.C.5
  • 14
    • 84888382759 scopus 로고    scopus 로고
    • Nonlinear normal modes of a full-scale aircraft
    • 10.2514/1.C031918
    • Kerschen G, Peeters M, Golinval JC, Stephan C (2013) Nonlinear normal modes of a full-scale aircraft. AIAA Journal Aircr 50:1409-1419
    • (2013) AIAA J , vol.50 , pp. 1409-1419
    • Kerschen, G.1    Peeters, M.2    Golinval, J.C.3    Stephan, C.4
  • 15
    • 33748795371 scopus 로고    scopus 로고
    • Nonlinear normal modes for damped geometrically nonlinear systems: Application to reduced-order modelling of harmonically forced structures
    • 2006JSV.298.958T 10.1016/j.jsv.2006.06.032
    • Touzé C, Amabili M (2006) Nonlinear normal modes for damped geometrically nonlinear systems: Application to reduced-order modelling of harmonically forced structures. J Sound Vib 298(4-5):958-981
    • (2006) J Sound Vib , vol.298 , Issue.4-5 , pp. 958-981
    • Touzé, C.1    Amabili, M.2
  • 16
    • 0029388116 scopus 로고
    • Nonlinear normal modes, invariance, and modal dynamics approximations of nonlinear systems
    • 1369226
    • Boivin N, Pierre C, Shaw SW (1995) Nonlinear normal modes, invariance, and modal dynamics approximations of nonlinear systems. Nonlinear Dyn 8:32
    • (1995) Nonlinear Dynamics , vol.8 , pp. 32
    • Boivin, N.1    Pierre, C.2    Shaw, S.W.3
  • 17
    • 0030173462 scopus 로고    scopus 로고
    • Normal modes for piecewise linear vibratory systems
    • 10.1007/BF00045454 1392618
    • Chen S-L, Shaw SW (1996) Normal modes for piecewise linear vibratory systems. Nonlinear Dyn 10:135-164
    • (1996) Nonlinear Dynamics , vol.10 , pp. 135-164
    • Chen, S.-L.1    Shaw, S.W.2
  • 18
    • 84905117326 scopus 로고    scopus 로고
    • Non-linear modal analysis of the forced response of structural systems
    • Boivin N, Pierre C, Shaw SW (1996) Non-linear modal analysis of the forced response of structural systems. AIAA J 31:22
    • (1996) AIAA J , vol.31 , pp. 22
    • Boivin, N.1    Pierre, C.2    Shaw, W.3
  • 19
    • 0000992329 scopus 로고
    • Non-linear modal analysis of structural systems featuring internal resonances
    • 10.1006/jsvi.1995.0201
    • Boivin N, Pierre C, Shaw SW (1995) Non-linear modal analysis of structural systems featuring internal resonances. J Sound Vib 182:6
    • (1995) J Sound Vib , vol.182 , pp. 6
    • Boivin, N.1    Pierre, C.2    Shaw, S.W.3
  • 20
    • 0037474503 scopus 로고    scopus 로고
    • A new Galerkin-based approach for accurate non-linear normal modes through invariant manifolds
    • 2002JSV.249.971P 10.1006/jsvi.2001.3914 1237.70100 1894121
    • Pesheck E, Pierre C, Shaw SW (2002) A new Galerkin-based approach for accurate non-linear normal modes through invariant manifolds. J Sound Vib 249(5):971-993
    • (2002) J Sound Vib , vol.249 , Issue.5 , pp. 971-993
    • Pesheck, E.1    Pierre, C.2    Shaw, S.W.3
  • 22
    • 2142657195 scopus 로고    scopus 로고
    • Large-amplitude non-linear normal modes of piecewise linear systems
    • 2004JSV.272.869J 10.1016/S0022-460X(03)00497-8 2049828
    • Jiang D, Pierre C, Shaw SW (2004) Large-amplitude non-linear normal modes of piecewise linear systems. J Sound Vib 272(3-5):869-891
    • (2004) J Sound Vib , vol.272 , Issue.3-5 , pp. 869-891
    • Jiang, D.1    Pierre, C.2    Shaw, S.W.3
  • 23
    • 26444518712 scopus 로고    scopus 로고
    • Nonlinear normal modes for vibratory systems under harmonic excitation
    • 2005JSV.288.791J 10.1016/j.jsv.2005.01.009
    • Jiang D, Pierre C, Shaw SW (2005) Nonlinear normal modes for vibratory systems under harmonic excitation. J Sound Vib 288(4-5):791-812
    • (2005) J Sound Vib , vol.288 , Issue.4-5 , pp. 791-812
    • Jiang, D.1    Pierre, C.2    Shaw, S.W.3
  • 24
    • 0035410005 scopus 로고    scopus 로고
    • Nonlinear modal analysis of structural systems using multi-mode invariant manifolds
    • 10.1023/A:1012910918498 1028.74025
    • Pesheck E, Boivin N, Pierre C, Shaw SW (2001) Nonlinear modal analysis of structural systems using multi-mode invariant manifolds. Nonlinear Dyn 25:183-205
    • (2001) Nonlinear Dyn , vol.25 , pp. 183-205
    • Pesheck, E.1    Bovine, N.2    Pierre, C.3    Shaw, S.W.4
  • 25
    • 13544274198 scopus 로고    scopus 로고
    • The construction of non-linear normal modes for systems with internal resonance
    • 10.1016/j.ijnonlinmec.2004.08.010 05138624
    • Jiang D, Pierre C, Shaw SW (2005) The construction of non-linear normal modes for systems with internal resonance. Int J Non-linear Mech 40(5):729-746
    • (2005) Int J Non-linear Mech , vol.40 , Issue.5 , pp. 729-746
    • Jiang, D.1    Pierre, C.2    Shaw, S.W.3
  • 26
    • 77956186192 scopus 로고    scopus 로고
    • Nonlinear normal modes of a rotating shaft based on the invariant manifold method
    • 10.1155/S1023621X04000338
    • Legrand M, Jiang D, Pierre C, Shaw SW (2004) Nonlinear normal modes of a rotating shaft based on the invariant manifold method. Int J Rotat Mach 10(4):319-335
    • (2004) Int J Rotat Mach , vol.10 , Issue.4 , pp. 319-335
    • Legrand, M.1    Jiang, D.2    Pierre, C.3    Shaw, S.W.4
  • 27
    • 84875260309 scopus 로고    scopus 로고
    • On the numerical computation of nonlinear normal modes for reduced-order modelling of conservative vibratory systems
    • 2013MSSP.36.520B 10.1016/j.ymssp.2012.10.016
    • Blanc F, Touzé C, Mercier JF, Ege K, Bonnet Ben-Dhia AS (2013) On the numerical computation of nonlinear normal modes for reduced-order modelling of conservative vibratory systems. Mech Syst Signal Process 36(2):520-539
    • (2013) Mech Syst Signal Process , vol.36 , Issue.2 , pp. 520-539
    • Blanc, F.1    Touzé, C.2    Mercier, J.F.3    Ege, K.4    Bonnet Ben-Dhia, A.S.5
  • 28
    • 24144498757 scopus 로고    scopus 로고
    • A new formulation for the existence and calculation of nonlinear normal modes
    • 2005JSV.287.545B 10.1016/j.jsv.2004.11.014 1243.70029 2173870
    • Bellizzi S, Bouc R (2005) A new formulation for the existence and calculation of nonlinear normal modes. J Sound Vib 287(3):545-569
    • (2005) J Sound Vib , vol.287 , Issue.3 , pp. 545-569
    • Bellizzi, S.1    Bouc, R.2
  • 29
    • 33845865823 scopus 로고    scopus 로고
    • An amplitude-phase formulation for nonlinear modes and limit cycles through invariant manifolds
    • 2007JSV.300.896B 10.1016/j.jsv.2006.09.004
    • Bellizzi S, Bouc R (2007) An amplitude-phase formulation for nonlinear modes and limit cycles through invariant manifolds. J Sound Vib 300(3-5):896-915
    • (2007) J Sound Vib , vol.300 , Issue.3-5 , pp. 896-915
    • Bellizzi, S.1    Bouc, R.2
  • 30
    • 63549092696 scopus 로고    scopus 로고
    • Complex non-linear modal analysis for mechanical systems: Application to turbomachinery bladings with friction interfaces
    • 2009JSV.322.1009L 10.1016/j.jsv.2008.11.044
    • Laxalde D, Thouverez F (2009) Complex non-linear modal analysis for mechanical systems: application to turbomachinery bladings with friction interfaces. J Sound Vib 322(4-5):1009-1025
    • (2009) Journal of Sound and Vibration , vol.322 , Issue.4-5 , pp. 1009-1025
    • Laxalde, D.1    Thouverez, F.2
  • 33
    • 1842787949 scopus 로고    scopus 로고
    • Automatic mesh update with the solid-extension mesh moving technique
    • 2004CMAME.193.2019S 10.1016/j.cma.2003.12.046 1067.74587
    • Stein K, Tezduyar TE, Benney R (2004) Automatic mesh update with the solid-extension mesh moving technique. Comput Methods Appl Mech Eng 193(21-22):2019-2032
    • (2004) Comput Methods Appl Mech Eng , vol.193 , Issue.21-22 , pp. 2019-2032
    • Stein, K.1    Tezduyar, T.E.2    Benney, R.3
  • 34
    • 1842685591 scopus 로고    scopus 로고
    • Finite element mesh update methods for fluid-structure interaction simulations
    • 10.1016/j.finel.2003.05.001
    • Xu Z, Accorsi M (2004) Finite element mesh update methods for fluid-structure interaction simulations. Finite Elem Anal Des 40(9-10):1259-1269
    • (2004) Finite Elem Anal des , vol.40 , Issue.9-10 , pp. 1259-1269
    • Xu, Z.1    Accorsi, M.2
  • 37
    • 0019607241 scopus 로고
    • Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
    • 1982CMAME.32.199B 10.1016/0045-7825(82)90071-8 0497.76041 679322
    • Brooks AN, Hughes TJR (1982) Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comput Methods Appl Mech Eng 32(1-3):199-259
    • (1982) Comput Methods Appl Mech Eng , vol.32 , Issue.1-3 , pp. 199-259
    • Brooks, A.N.1    Hughes, T.J.R.2
  • 38
    • 0021497923 scopus 로고
    • Finite element methods for first-order hyperbolic systems with particular emphasis on the compressible Euler equations
    • 1984CMAME.45.217H 10.1016/0045-7825(84)90157-9 0542.76093 759810
    • Hughes TJR, Tezduyar TE (1984) Finite element methods for first-order hyperbolic systems with particular emphasis on the compressible Euler equations. Comput Methods Appl Mech Eng 45(1-3):217-284
    • (1984) Comput Methods Appl Mech Eng , vol.45 , Issue.1-3 , pp. 217-284
    • Hughes, T.J.R.1    Tezduyar, T.E.2
  • 39
    • 10044269430 scopus 로고    scopus 로고
    • Asymptotic non-linear normal modes for large-amplitude vibrations of continuous structures
    • 10.1016/j.compstruc.2004.09.003
    • Touzé C, Thomas O, Huberdeau A (2004) Asymptotic non-linear normal modes for large-amplitude vibrations of continuous structures. Comput Struct 82(31-32):2671-2682
    • (2004) Comput Struct , vol.82 , Issue.31-32 , pp. 2671-2682
    • Touzé, C.1    Thomas, O.2    Huberdeau, A.3
  • 41
    • 0003584080 scopus 로고    scopus 로고
    • Practical bifurcation and stability analysis, volume 5 of Interdisciplinary
    • Springer, New York
    • Seydel R (2010) Practical bifurcation and stability analysis, volume 5 of Interdisciplinary Applied Mathematics. Springer, New York
    • (2010) Applied Mathematics
    • Seydel, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.