Modal analysis-based reduced-order models for nonlinear structures-an invariant manifold approach

Shock and Vibration Digest

Volumn 31, Issue 1, 1999, Pages 3-16

  Shaw, Steven W ^a   Pierre, Christophe ^b   Pesheck, Eric ^b  

^a Michigan State University   (United States)

^b UNIVERSITY OF MICHIGAN   (United States)

Author keywords

Invariant manifolds; Modal analysis; Nonlinear vibration; Normal modes

Indexed keywords

DEGREES OF FREEDOM (MECHANICS); EQUATIONS OF MOTION; MATHEMATICAL MODELS; MODAL ANALYSIS; NONLINEAR SYSTEMS;

INVARIANT MANIFOLDS; NONLINEAR VIBRATION SYSTEM;

VIBRATIONS (MECHANICAL);

EID: 0031599011     PISSN: 05831024     EISSN: None     Source Type: Journal    
DOI: 10.1177/058310249903100101     Document Type: Article

References (18)

1. Boivin, N., 1995, "Non-linear modal analysis of structural systems using invariant manifolds," Ph.D. dissertation, University of Michigan.
2. Boivin, N., Pierre, C., and Shaw, S. W., 1994, "Non-linear modal analysis of structural systems using multi-mode invariant manifolds" (paper no. 94-1672), Proceedings of the AIAA Dynamics Specialists Conference, Hilton Head, South Carolina, April.
3. Boivin, N., Pierre, C, and Shaw, S. W., 1995, "Non-linear modal analysis of structural systems featuring internal resonances," J. Sound Vibration 182, 336-341.
4. Boivin, N., Pierre, G, and Shaw, S. W., 1996, "Non- linear modal analysis of forced response of structural systems" (paper no. 96-1250), Proceedings of the AIAA Dynamics Specialists Conference, Salt Lake City, Utah.
5. Feeny, B. F., 1997, "Interpreting proper orthogonal modes in vibrations" (paper no. VIB-3955), Proceedings of DET'97, 1997 ASME Design Engineering Technical Conference, Sacramento, California, September.
6. Hsieh, S.-R., Shaw, S. R., and Pierre, C., 1994, "Normal modes for large amplitude vibration of a cantilever beam," Int. J. Solids Struct. 31, 1981-2014.
7. King, M. E., and Vakakis, A. F., 1996, "An energy based formulation for computing nonlinear normal modes in undamped continuous systems," J. Vibration Acoustics, Trans. ASME 116, 332-340.
8. Nayfeh, A. H., 1995, "On direct methods for constructing nonlinear normal modes of continuous systems," J. Vibration Control 1, 389-430.
9. Nayfeh, A. H., Chin, C., and Nayfeh, S. A., 1996, "On nonlinear normal modes of systems with internal resonance," J. Vibration Acoustics, Trans. ASME 118, 340-345.
10. Pesheck, E., and Pierre, G, 1997, "A global methodology for the modal reduction of large nonlinear systems containing quadradic and cubic nonlinearities" (paper no. VIB-3952), Proceedings of DET'97, 1997 ASME Design Engineering Technical Conference, Sacramento, California, September.
11. Rosenberg, R. M., 1966, "On nonlinear vibrations of systems with many degrees of freedom," Advances Appl. Mech. 9, 155-242.
12. Shaw, S. W., 1994, "An invariant approach to nonlinear normal modes of vibration," J. Nonlinear Sci. 4, 419-448.
13. Shaw, S. W., and Pierre, C., 1993, "Normal modes for non-linear vibratory systems," J. Sound Vibration 164, 85-124.
14. Shaw, S. W., and Pierre, C., 1994, "Normal modes of vibration for non-linear continuous systems," J. Sound Vibration 169, 319-347.
15. Slater, J. C., 1996, "A numerical method for determining nonlinear normal modes," Nonlinear Dynamics 10,29-30.
16. Troger, H., Steindl, A., and Zemann, J., 1997, "Improved galerkin methods for the dimension reduction of nonlinear dynamical systems," Proceedings of the IUTAM Symposium of Applications of Nonlinear and Chaotic Dynamics in Mechanics, Ithaca, New York, July-August.
17. Vakakis, A. F., 1997, "Non-linear normal modes (nnms) and their applications in vibration theory: An overview," Mechanical Sys. Signal Processing 11, 3-22.
18. Vakakis, A. F., Manevitch, L. I., Mikhlin, Y. V., Pilipchuck, V. N., and Zevin, A. A., 1996, Normal Modes and Localization in Nonlinear Systems, John Wiley & Sons, New York.