Non-linear modal analysis of a rotating beam

International Journal of Non-Linear Mechanics

Volumn 46, Issue 6, 2011, Pages 877-897

  Arvin, H ^a   Bakhtiari Nejad, F ^a  

^a AMIRKABIR UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Internal resonance; Non linear normal mode; Rotating beam; Stability

Indexed keywords

AXIAL DISPLACEMENTS; COUPLED MODE; DYNAMIC CHARACTERISTICS; GALERKIN DISCRETIZATION; GEOMETRIC NONLINEARITY; HAMILTON'S PRINCIPLE; INTERNAL RESONANCE; METHOD OF MULTIPLE SCALE; NON-LINEAR; NON-LINEAR NORMAL MODE; NON-LINEAR VIBRATIONS; NONLINEAR NORMAL MODES; PHASE PORTRAIT; POINCARE SECTIONS; ROTATING BEAM; SPECTRUM DIAGRAM; STRAIN-DISPLACEMENT RELATION; TRANSVERSE MODE; VON KARMAN;

ANTENNAS; DISCRETE EVENT SIMULATION; EQUATIONS OF MOTION; MODAL ANALYSIS; ORDINARY DIFFERENTIAL EQUATIONS; RESONANCE; VIBRATION ANALYSIS;

ROTATION;

EID: 79957486233     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijnonlinmec.2011.03.017     Document Type: Article

References (17)

1. R.M. Rosenberg On nonlinear vibrations of systems with many degrees of freedom Adv. Appl. Mech. 9 1966 155 242
2. S.W. Shaw, and C. Pierre Normal modes of vibration for non-linear continuous systems J. Sound Vib. 169 1994 319 347
3. M.E. King, and A.F. Vakakis Energy-based formulation for computing nonlinear normal modes in undamped continuous systems J. Vib. Acoust. 116 3 1994 332 340
4. A.H. Nayfeh, and S.A. Nayfeh On nonlinear modes of continuous systems ASME J. Vib. Acoust. 116 1994 129 136
5. A.H. Nayfeh, and S.A. Nayfeh Nonlinear normal modes of continuous system with quadratic nonlinearities ASME J. Vib. Acoust. 117 1995 199 205
6. C.E.N. Mazzilli, C.T. Sanches, O.G.P. Baracho Neto, M. Wiercigroch, and M. Keber Non-linear modal analysis for beams subjected to axial loads: analytical and finite-element solutions Int. J. Non-Linear Mech. 43 2008 551 561
7. A.H. Nayfeh, W. Lacarbonara, and C. Chin Nonlinear normal modes of buckled beams: three-to-one and one-to-one internal resonances Non-linear Dyn. 18 1999 253 273
8. W. Lacarbonara, G. Rega, and A.H. Nayfeh Resonant non-linear normal modes. part i: analytical treatment for structural one-dimensional systems Int. J. Non-Linear Mech. 38 2003 851 872 (Pubitemid 35384412)
9. X. Li, J.C. Ji, and C.H. Hansen Non-linear normal modes and their bifurcation of a two dof system with quadratic and cubic non-linearity Int. J. Non-Linear Mech. 41 2006 1028 1038
10. M.R.M. Crespo da Silva, and D.H. Hodges Nonlinear flexure and torsion of rotating beams with application to helicopter rotor blades - I. Formulation Vertica 10 2 1986 151 169
11. M.R.M. Crespo da Silva, and D.H. Hodges Nonlinear flexure and torsion of rotating beams with application to helicopter rotor blades - II. Response and stability results Vertica 10 2 1986 171 186
12. E. Pesheck, C. Pierre, S. Shaw, Modal reduction of a nonlinear rotating beam through nonlinear normal modes, in: Proceedings of the ASME Design Engineering Technical Conferences, September 1215, Las Vegas, Nevada, 1999.
13. E. Pesheck, C. Pierre, and S. Shaw Accurate reduced-order models for a simple rotor blade model using nonlinear normal modes Math. Comput. Model 33 2001 1085 1097 (Pubitemid 32329019)
14. E. Pesheck, C. Pierre, and S. Shaw Modal reduction of a nonlinear rotating beam through nonlinear normal modes ASME J. Vib. Acoust. 124 2002 229 235
15. P. Apiwattanalunggarn, S. Shaw, C. Pierre, and D. Jiang Finite-element-based nonlinear modal reduction of a rotating beam with large-amplitude motion J. Vib. Control 9 2003 235 263
16. 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 2005 729 746 (Pubitemid 40219752)
17. S.K. Das, P.C. Ray, and G. Pohit The construction of non-linear normal modes for systems with internal resonance J. Vib. Control 11 2005 1511 1533