Non-linear normal modes and their bifurcation of a two DOF system with quadratic and cubic non-linearity

International Journal of Non-Linear Mechanics

Volumn 41, Issue 9, 2006, Pages 1028-1038

  Li, Xinye ^a   Ji, J C ^b   Hansen, Colin H ^b  

^a HEBEI UNIVERSITY OF TECHNOLOGY   (China)

^b UNIVERSITY OF ADELAIDE   (Australia)

Author keywords

Internal resonance; Mode bifurcation; Mode coupling; Non linear normal modes; The method of multiple scales

Indexed keywords

BIFURCATION (MATHEMATICS); DEGREES OF FREEDOM (MECHANICS); EQUATIONS OF MOTION; LARGE SCALE SYSTEMS; QUADRATIC PROGRAMMING; RESONANCE;

INTERNAL RESONANCE; MODE BIFURCATION; MODE COUPLING; NON-LINEAR NORMAL MODES (NNM);

NONLINEAR SYSTEMS;

EID: 33846448490     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijnonlinmec.2005.12.005     Document Type: Article

References (10)

1. Rosenberg R.M. On nonlinear vibrations of systems with many DOF. Adv. Appl. Mech. 9 (1966) 155-242
2. Shaw S.W., and Pierre C. Nonlinear normal modes and invariant manifolds. J. Sound Vib. 150 (1991) 170-173
3. King M.E., and Vakakis A.F. An energy-based formulation for computing nonlinear normal modes in undamped continuous systems. J. Vib. Acoust. 116 (1994) 332-340
4. Nayfeh A.H. On direct methods for constructing nonlinear modes of continuous systems. J. Vib. Control 1 (1995) 389-430
5. Nayfeh A.H., and Nayfeh S.A. Nonlinear normal modes of a continuous system with quadratic nonlinearity. J. Vib. Acoust. 117 (1995) 199-205
6. Bhattacharyya R., Jain P., and Nair A. Normal mode localization for a two degrees-of-freedom system with quadratic and cubic nonlinearities. J. Sound Vib. 249 (2002) 909-919
7. Balthazar J.M., and Brasil R.M.L.R.F. On normal modes of a two DOF model of a structure with quadratic nonlinearities. J. Sound Vib. 182 (1995) 659-664
8. Nayfeh A.H. Perturbation Methods (1973), Springer, New York
9. Nayfeh A.H., and Moke D.T. Nonlinear Oscillations (1979), Springer, New York
10. Nayfeh A.H., Lacarbonara W., and Chin C. Nonlinear normal modes of buckled beams: three-to-one and one-to-one internal resonance. Nonlinear Dyn. 18 (1999) 253-273