-
1
-
-
85024529756
-
The normal modes of nonlinear n-degree-of-freedom systems
-
R.M. Rosenberg The normal modes of nonlinear n-degree-of-freedom systems J. Appl. Mech. 29 1962 7 14
-
(1962)
J. Appl. Mech.
, vol.29
, pp. 7-14
-
-
Rosenberg, R.M.1
-
2
-
-
33645049419
-
On non-linear vibrations of systems with many degrees of freedom
-
R.M. Rosenberg On non-linear vibrations of systems with many degrees of freedom Adv. Appl. Mech. 9 1966 155 242
-
(1966)
Adv. Appl. Mech.
, vol.9
, pp. 155-242
-
-
Rosenberg, R.M.1
-
3
-
-
0029388116
-
Non-linear normal modes, invariance, and modal dynamics approximations of non-linear systems
-
N. Boivin, C. Pierre, and S. Shaw Non-linear normal modes, invariance, and modal dynamics approximations of non-linear systems Nonlinear Dyn. 8 1995 315 346
-
(1995)
Nonlinear Dyn.
, vol.8
, pp. 315-346
-
-
Boivin, N.1
Pierre, C.2
Shaw, S.3
-
4
-
-
0037262542
-
Fitting measured frequency response using non-linear normal modes
-
C. Gibert Fitting measured frequency response using non-linear normal modes Mech. Syst. Signal Process. 17 1 2003 211 218
-
(2003)
Mech. Syst. Signal Process.
, vol.17
, Issue.1
, pp. 211-218
-
-
Gibert, C.1
-
6
-
-
53849093038
-
Non-linear normal modes, part i a useful framework for the structural dynamicist
-
G. Kerschen, M. Peeters, J.C. Golinval, and A.F. Vakakis Non-linear normal modes, part I a useful framework for the structural dynamicist Mech. Syst. Signal Process. 23 1 2009 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
-
7
-
-
63549092696
-
Complex non-linear modal analysis for mechanical systems application to turbomachinery bladings with friction interface
-
D. Laxalde, and F. Thouverez Complex non-linear modal analysis for mechanical systems application to turbomachinery bladings with friction interface J. Sound Vib. 322 4-5 2009 1009 1025
-
(2009)
J. Sound Vib.
, vol.322
, Issue.45
, pp. 1009-1025
-
-
Laxalde, D.1
Thouverez, F.2
-
8
-
-
0027911991
-
Normal modes for non-linear vibratory systems
-
S.W. Shaw, and C. Pierre Normal modes for non-linear vibratory systems J. Sound Vib. 164 1 1993 85 124
-
(1993)
J. Sound Vib.
, vol.164
, Issue.1
, pp. 85-124
-
-
Shaw, S.W.1
Pierre, C.2
-
9
-
-
0028197991
-
On nonlinear normal modes of continuous systems
-
A.H. Nayfeh, and S.A. Nayfeh On nonlinear normal modes of continuous systems Trans. ASME/J. Vib. Acoust. 116 1994 129 136
-
(1994)
Trans. ASME/J. Vib. Acoust.
, vol.116
, pp. 129-136
-
-
Nayfeh, A.H.1
Nayfeh, S.A.2
-
10
-
-
0032097205
-
Reduced-order models of weakly non-linear spatially continuous systems
-
A.H. Nayfeh Reduced-order models of weakly non-linear spatially continuous systems Nonlinear Dyn. 16 1998 105 125
-
(1998)
Nonlinear Dyn.
, vol.16
, pp. 105-125
-
-
Nayfeh, A.H.1
-
12
-
-
0011646339
-
Reduction methods for nonlinear vibrations of spatially continuous systems with initial curvature
-
G. Rega, W. Lacarbonara, and A.H. Nayfeh Reduction methods for nonlinear vibrations of spatially continuous systems with initial curvature Solid Mech. Appl. 77 2000 235 246
-
(2000)
Solid Mech. Appl.
, vol.77
, pp. 235-246
-
-
Rega, G.1
Lacarbonara, W.2
Nayfeh, A.H.3
-
13
-
-
2342517458
-
Hardening/softening behaviour in non-linear oscillations of structural systems using non-linear normal modes
-
C. Touzé, O. Thomas, and A. Chaigne Hardening/softening behaviour in non-linear oscillations of structural systems using non-linear normal modes J. Sound Vib. 273 1-2 2004 77 101
-
(2004)
J. Sound Vib.
, vol.273
, Issue.12
, pp. 77-101
-
-
Touzé, C.1
Thomas, O.2
Chaigne, A.3
-
14
-
-
10044269430
-
Asymptotic non-linear normal modes for large amplitude vibrations of continuous structures
-
C. Touzé, O. Thomas, and A. Huberdeau Asymptotic non-linear normal modes for large amplitude vibrations of continuous structures Comput. Struct. 82 31-32 2004 2671 2682
-
(2004)
Comput. Struct.
, vol.82
, Issue.3132
, pp. 2671-2682
-
-
Touzé, C.1
Thomas, O.2
Huberdeau, A.3
-
15
-
-
18444364818
-
Order reduction of nonlinear systems with time periodic coefficients using invariant manifolds
-
S.C. Sinha, S. Redkar, and E.A. Butcher Order reduction of nonlinear systems with time periodic coefficients using invariant manifolds J. Sound Vib. 284 3-5 2005 985 1002
-
(2005)
J. Sound Vib.
, vol.284
, Issue.35
, pp. 985-1002
-
-
Sinha, S.C.1
Redkar, S.2
Butcher, E.A.3
-
16
-
-
34547131037
-
Reduced-order models for non-linear vibrations of fluid-filled circular cylindrical shells comparison of pod and asymptotic non-linear normal modes methods
-
M. Amabili, and C. Touzé Reduced-order models for non-linear vibrations of fluid-filled circular cylindrical shells comparison of pod and asymptotic non-linear normal modes methods J. Fluids Struct. 23 6 2007 885 903
-
(2007)
J. Fluids Struct.
, vol.23
, Issue.6
, pp. 885-903
-
-
Amabili, M.1
Touzé, C.2
-
17
-
-
40349092905
-
Reduced-order models for large-amplitude vibrations of shells including in-plane inertia
-
C. Touzé, M. Amabili, and O. Thomas Reduced-order models for large-amplitude vibrations of shells including in-plane inertia Comput. Methods Appl. Mech. Eng. 197 21-24 2008 2030 2045
-
(2008)
Comput. Methods Appl. Mech. Eng.
, vol.197
, Issue.2124
, pp. 2030-2045
-
-
Touzé, C.1
Amabili, M.2
Thomas, O.3
-
18
-
-
67349212595
-
Nonlinear modes of clarinet-like musical instruments
-
D. Noreland, S. Bellizzi, C. Vergez, and R. Bouc Nonlinear modes of clarinet-like musical instruments J. Sound Vib. 324 3-5 2009 983 1002
-
(2009)
J. Sound Vib.
, vol.324
, Issue.35
, pp. 983-1002
-
-
Noreland, D.1
Bellizzi, S.2
Vergez, C.3
Bouc, R.4
-
19
-
-
0038005081
-
Dynamics of linear discrete systems connected to local, essentially non-linear attachments
-
A.F. Vakakis, L.I. Manevitch, O. Gendelman, and L. Bergman Dynamics of linear discrete systems connected to local, essentially non-linear attachments J. Sound Vib. 264 2003 559 577
-
(2003)
J. Sound Vib.
, vol.264
, pp. 559-577
-
-
Vakakis, A.F.1
Manevitch, L.I.2
Gendelman, O.3
Bergman, L.4
-
20
-
-
27544508422
-
Energy transfers in a system of two coupled oscillators with essential nonlinearity 1:1 resonance manifold and transient bridging orbits
-
G. Kerschen, A.F. Vakakis, Y.S. Lee, D.M. McFarland, J.J. Kowtko, and L.A. Bergman Energy transfers in a system of two coupled oscillators with essential nonlinearity 1:1 resonance manifold and transient bridging orbits Nonlinear Dyn. 42 2005 283 303
-
(2005)
Nonlinear Dyn.
, vol.42
, pp. 283-303
-
-
Kerschen, G.1
Vakakis, A.F.2
Lee, Y.S.3
McFarland, D.M.4
Kowtko, J.J.5
Bergman, L.A.6
-
21
-
-
18844398348
-
Energy pumping for a larger span of energy
-
E. Gourdon, and C.H. Lamarque Energy pumping for a larger span of energy J. Sound Vib. 285 2005 711 720
-
(2005)
J. Sound Vib.
, vol.285
, pp. 711-720
-
-
Gourdon, E.1
Lamarque, C.H.2
-
22
-
-
77649337670
-
-
Springer New York
-
A.F. Vakakis, O.V. Gendelman, L.A. Bergman, D.M. McFarland, G. Kerschen, and Y.S. Lee Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems I 2008 Springer New York
-
(2008)
Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems i
-
-
Vakakis, A.F.1
Gendelman, O.V.2
Bergman, L.A.3
McFarland, D.M.4
Kerschen, G.5
Lee, Y.S.6
-
23
-
-
77649337670
-
-
Springer New York
-
A.F. Vakakis, O.V. Gendelman, L.A. Bergman, D.M. McFarland, G. Kerschen, and Y.S. Lee Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems II 2008 Springer New York
-
(2008)
Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems II
-
-
Vakakis, A.F.1
Gendelman, O.V.2
Bergman, L.A.3
McFarland, D.M.4
Kerschen, G.5
Lee, Y.S.6
-
25
-
-
0015465649
-
On periodic solutions close to rectilinear normal vibration modes
-
L.I. Manevitch, and Yu.V. Mikhlin On periodic solutions close to rectilinear normal vibration modes J. Appl. Math. Mech. (PMM) 36 6 1972 1051 1058
-
(1972)
J. Appl. Math. Mech. (PMM)
, vol.36
, Issue.6
, pp. 1051-1058
-
-
Manevitch, L.I.1
Mikhlin, Yu.V.2
-
26
-
-
0000809158
-
A direct method for non-linear normal modes
-
R.H. Rand A direct method for non-linear normal modes Int. J. Non-linear Mech. 9 1974 363 368
-
(1974)
Int. J. Non-linear Mech.
, vol.9
, pp. 363-368
-
-
Rand, R.H.1
-
27
-
-
0028461550
-
Energy-based formulation for computing nonlinear normal modes in undamped continuous systems
-
M.E. King, and A.F. Vakakis Energy-based formulation for computing nonlinear normal modes in undamped continuous systems J. Vib. Acoust. 116 1994 332 340
-
(1994)
J. Vib. Acoust.
, vol.116
, pp. 332-340
-
-
King, M.E.1
Vakakis, A.F.2
-
28
-
-
0030230830
-
Normal vibrations of a general class of conservative oscillators
-
Yu.V. Mikhlin Normal vibrations of a general class of conservative oscillators Non-linear Dyn. 11 1996 1 15
-
(1996)
Non-linear Dyn.
, vol.11
, pp. 1-15
-
-
Mikhlin, Yu.V.1
-
29
-
-
0026420003
-
Non-linear normal modes and invariant manifolds
-
S.W. Shaw, and C. Pierre Non-linear normal modes and invariant manifolds J. Sound Vib. 150 1 1991 170 173
-
(1991)
J. Sound Vib.
, vol.150
, Issue.1
, pp. 170-173
-
-
Shaw, S.W.1
Pierre, C.2
-
32
-
-
0000077159
-
Solutions d'un système d'équations différentielles dans le voisinage de valeurs singulières
-
H. Dulac Solutions d'un système d'équations différentielles dans le voisinage de valeurs singulières Bulletin de la Société Mathématique de France 40 1912 324 383
-
(1912)
Bulletin de la Société Mathématique de France
, vol.40
, pp. 324-383
-
-
Dulac, H.1
-
33
-
-
0026223029
-
Analysis of non-linear dynamical systems by the normal form theory
-
L. Jézéquel, and C.H. Lamarque Analysis of non-linear dynamical systems by the normal form theory J. Sound Vib. 149 3 1991 429 459
-
(1991)
J. Sound Vib.
, vol.149
, Issue.3
, pp. 429-459
-
-
Jézéquel, L.1
Lamarque, C.H.2
-
34
-
-
33748795371
-
Non-linear normal modes for damped geometrically non-linear systems application to reduced-order modeling of harmonically forced structures
-
C. Touzé, and M. Amabili Non-linear normal modes for damped geometrically non-linear systems application to reduced-order modeling of harmonically forced structures J. Sound Vib. 298 4-5 2006 958 981
-
(2006)
J. Sound Vib.
, vol.298
, Issue.45
, pp. 958-981
-
-
Touzé, C.1
Amabili, M.2
-
35
-
-
0030780655
-
Non-linear normal modes (nnms) and their application in vibration theory an overview
-
A.F. Vakakis Non-linear normal modes (nnms) and their application in vibration theory an overview Mech. Syst. Signal Process. 11 1 1997 3 22
-
(1997)
Mech. Syst. Signal Process.
, vol.11
, Issue.1
, pp. 3-22
-
-
Vakakis, A.F.1
-
36
-
-
14744299273
-
Geodesics, nonlinear normal modes of conservative vibratory systems and decomposition method
-
X. Zhang Geodesics, nonlinear normal modes of conservative vibratory systems and decomposition method J. Sound Vib. 282 2005 971 989
-
(2005)
J. Sound Vib.
, vol.282
, pp. 971-989
-
-
Zhang, X.1
-
37
-
-
0022191004
-
The calculation of strongly nonlinear systems close to vibration-impact systems
-
V.N. Pilipchuk The calculation of strongly nonlinear systems close to vibration-impact systems Prikl. Mat. Mech. 49 5 1985 572 578
-
(1985)
Prikl. Mat. Mech.
, vol.49
, Issue.5
, pp. 572-578
-
-
Pilipchuk, V.N.1
-
38
-
-
0002900162
-
A transformation for vibrating systems based on a non-smooth periodic pair of functions
-
(in Russian)
-
V.N. Pilipchuk A transformation for vibrating systems based on a non-smooth periodic pair of functions Dokl. An. Ukr. SSR 4 1988 37 40 (in Russian)
-
(1988)
Dokl. An. Ukr. SSR
, vol.4
, pp. 37-40
-
-
Pilipchuk, V.N.1
-
39
-
-
0006174897
-
Study of a class of subharmonic motions using a non-smooth temporal transformation (nstt)
-
V.N. Pilipchuk, A.F. Vakakis, and M.A.F. Azeez Study of a class of subharmonic motions using a non-smooth temporal transformation (nstt) Physica D 100 1997 145 164
-
(1997)
Physica D
, vol.100
, pp. 145-164
-
-
Pilipchuk, V.N.1
Vakakis, A.F.2
Azeez, M.A.F.3
-
40
-
-
18844436998
-
Complicated dynamics of a linear oscillator with a light, essentially non-linear attachment
-
Y.S. Lee, G. Kerschen, A.F. Vakakis, P. Panagopoulos, L. Bergman, and D.M. McFarland Complicated dynamics of a linear oscillator with a light, essentially non-linear attachment Physica D 204 2005 41 69
-
(2005)
Physica D
, vol.204
, pp. 41-69
-
-
Lee, Y.S.1
Kerschen, G.2
Vakakis, A.F.3
Panagopoulos, P.4
Bergman, L.5
McFarland, D.M.6
-
41
-
-
0030151935
-
A numerical method for determining nonlinear normal modes
-
J.C. Slater A numerical method for determining nonlinear normal modes Nonlinear Dyn. 10 1 1996 19 30
-
(1996)
Nonlinear Dyn.
, vol.10
, Issue.1
, pp. 19-30
-
-
Slater, J.C.1
-
43
-
-
33746882845
-
Two methods for the computation of nonlinear modes of vibrating systems at large amplitudes
-
R. Arquier, S. Bellizzi, R. Bouc, and B. Cochelin Two methods for the computation of nonlinear modes of vibrating systems at large amplitudes Comput. Struct. 84 24-25 2006 1565 1576
-
(2006)
Comput. Struct.
, vol.84
, Issue.2425
, pp. 1565-1576
-
-
Arquier, R.1
Bellizzi, S.2
Bouc, R.3
Cochelin, B.4
-
44
-
-
53849083425
-
Non-linear normal modes, part II toward a practical computation using numerical continuation techniques
-
M. Peeters, R. Viguié, G. Sérandour, G. Kerschen, and J.C. Golinval Non-linear normal modes, part II toward a practical computation using numerical continuation techniques Mech. Syst. Signal Process. 23 1 2009 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
-
45
-
-
0038194270
-
-
Concordia University
-
E.J. Doedel, R. Paffenroth, A.R. Champneys, T.F. Fairgrieve, Y.A. Kuznetsov, B.E. Oldeman, B. Sandstede, X. Wang, Auto 2000: Continuation and Bifurcation Software for Ordinary Differential Equations, Technical Report, Concordia University, 2002, available at 〈 http://www.cmvl.cs.concordia.ca/ auto/ 〉.
-
(2002)
Auto 2000: Continuation and Bifurcation Software for Ordinary Differential Equations, Technical Report
-
-
Doedel, E.J.1
Paffenroth, R.2
Champneys, A.R.3
Fairgrieve, T.F.4
Kuznetsov, Y.A.5
Oldeman, B.E.6
Sandstede, B.7
Wang, X.8
-
46
-
-
67349260182
-
A high-order purely frequency-based harmonic balance formulation for continuation of periodic solutions
-
B. Cochelin, and C. Vergez A high-order purely frequency-based harmonic balance formulation for continuation of periodic solutions J. Sound Vib. 324 1-2 2009 243 262
-
(2009)
J. Sound Vib.
, vol.324
, Issue.12
, pp. 243-262
-
-
Cochelin, B.1
Vergez, C.2
-
47
-
-
84875251936
-
-
Laboratoire de Mécanique et d'Acoustique (LMA), CNRS UPR 7051
-
S. Karkar, B. Cochelin, C. Vergez, O. Thomas, A. Lazarus, User Guide Manlab 2.0, Technical Report, Laboratoire de Mécanique et d'Acoustique (LMA), CNRS UPR 7051, 2002. Available at: 〈 http://manlab.lma.cnrs-mrs.fr/ 〉.
-
(2002)
User Guide Manlab 2.0, Technical Report
-
-
Karkar, S.1
Cochelin, B.2
Vergez, C.3
Thomas, O.4
Lazarus, A.5
-
48
-
-
8744230577
-
Matcont a MATLAB package for numerical bifurcation analysis of ODEs
-
A. Dhooge, W. Govaerts, and Y.A. Kuznetsov Matcont a MATLAB package for numerical bifurcation analysis of ODEs ACM Trans. Math. Software 29 2 2003 141 164 Available at: 〈 http://sourceforge.net/projects/matcont/ 〉
-
(2003)
ACM Trans. Math. Software
, vol.29
, Issue.2
, pp. 141-164
-
-
Dhooge, A.1
Govaerts, W.2
Kuznetsov, Y.A.3
-
49
-
-
0028203123
-
Normal modes of vibration for non-linear continuous systems
-
S.W. Shaw, and C. Pierre Normal modes of vibration for non-linear continuous systems J. Sound Vib. 169 3 1994 85 124
-
(1994)
J. Sound Vib.
, vol.169
, Issue.3
, pp. 85-124
-
-
Shaw, S.W.1
Pierre, C.2
-
50
-
-
0037474503
-
A new Galerkin-based approach for accurate non-linear normal modes through invariant manifolds
-
E. Pesheck, C. Pierre, and S. Shaw A new Galerkin-based approach for accurate non-linear normal modes through invariant manifolds J. Sound Vib. 249 5 2002 971 993
-
(2002)
J. Sound Vib.
, vol.249
, Issue.5
, pp. 971-993
-
-
Pesheck, E.1
Pierre, C.2
Shaw, S.3
-
51
-
-
2142657195
-
Large-amplitude non-linear normal modes of piecewise linear systems
-
D. Jiang, C. Pierre, and S. Shaw Large-amplitude non-linear normal modes of piecewise linear systems J. Sound Vib. 272 3-5 2004 869 891
-
(2004)
J. Sound Vib.
, vol.272
, Issue.35
, pp. 869-891
-
-
Jiang, D.1
Pierre, C.2
Shaw, S.3
-
52
-
-
26444518712
-
Nonlinear normal modes for vibratory systems under harmonic excitation
-
D. Jiang, C. Pierre, and S. Shaw Nonlinear normal modes for vibratory systems under harmonic excitation J. Sound Vib. 288 4-5 2005 791 812
-
(2005)
J. Sound Vib.
, vol.288
, Issue.45
, pp. 791-812
-
-
Jiang, D.1
Pierre, C.2
Shaw, S.3
-
53
-
-
13544274198
-
The construction of non-linear normal modes for systems with internal resonance
-
D. Jiang, C. Pierre, and S. Shaw The construction of non-linear normal modes for systems with internal resonance Int. J. Non-linear Mech. 40 5 2005 729 746
-
(2005)
Int. J. Non-linear Mech.
, vol.40
, Issue.5
, pp. 729-746
-
-
Jiang, D.1
Pierre, C.2
Shaw, S.3
-
54
-
-
84875249536
-
Computation of nonlinear normal modes of large structures: Application to a full-scale aircraft
-
Roma
-
M. Peeters, L. Renson, G. Kerschen, J.-C. Golinval, C. Stéphan, P. Lubrina, Computation of nonlinear normal modes of large structures: application to a full-scale aircraft, in: Proceedings of the Seventh Nonlinear Dynamics Conference, ENOC-2011, Roma, 2011.
-
(2011)
Proceedings of the Seventh Nonlinear Dynamics Conference, ENOC-2011
-
-
Peeters, M.1
-
57
-
-
84871017828
-
An upper bound for validity limits of asymptotic analytical approaches based on normal form theory, Non-linear Dynamics
-
C.-H. Lamarque, C. Touzé, O. Thomas, An upper bound for validity limits of asymptotic analytical approaches based on normal form theory, Non-linear Dynamics, Non-linear Dyn. 70 (3) (2012) 1931-1949.
-
(2012)
Non-linear Dyn.
, vol.70
, Issue.3
, pp. 1931-1949
-
-
Lamarque, H.C.1
-
58
-
-
67649202516
-
Modal analysis of a nonlinear periodic structure with cyclic symmetry
-
F. Georgiades, M. Peeters, G. Kerschen, J.C. Golinval, and M. Ruzzene Modal analysis of a nonlinear periodic structure with cyclic symmetry AIAA J. 47 2009 1014 1025
-
(2009)
AIAA J.
, vol.47
, pp. 1014-1025
-
-
Georgiades, F.1
Peeters, M.2
Kerschen, G.3
Golinval, J.C.4
Ruzzene, M.5
|