Nonlinear mode localization in systems governed by partial differential equations

Applied Mechanics Reviews

Volumn 49, Issue 2, 1996, Pages 87-99

  Vakakis, Alexander F ^a  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); EQUATIONS OF MOTION; NONLINEAR EQUATIONS; OSCILLATIONS; PARTIAL DIFFERENTIAL EQUATIONS; PERTURBATION TECHNIQUES;

NONLINEAR NORMAL MODE LOCALIZATION;

STRUCTURAL ANALYSIS;

EID: 0030079921     PISSN: 00036900     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.3101890     Document Type: Article

References (39)

1. Anderson PW (1958), Absence of diffusion in certain random lattices, Phys Rev, 109 (5), 1492-1505.
2. Hodges CH (1982), Confinement of vibration by structural irregularity, J Sound Vib, 82 (3), 411-424.
3. Pierre C and Dowell EH (1987), Localization of vibrations by structural irregularity, J Sound Vib, 114 (3), 549-564.
4. Kissel GJ (1988), Localization in Disordered Periodic Structures, PhD Thesis, Massachusetts Inst of Tech, Boston MA.
5. Pierre C and Cha P (1989), Strong mode localization in nearly periodic disordered structures. AIAA J, 27 (2), 227-241.
6. Pierre C (1989), Curve veering and mode localization in a buckled problem, J Appl Math Phys (ZAMP), 40, 758-761.
7. Cornwell PJ and Bendiksen OO (1989). Localization of vibrations in large space reflectors, AIAA J, 27 (2), 219-226.
8. Keane AJ and Price WG (1989), On the vibrations of mono-coupled periodic and near-periodic structures, J Sound Vib, 128 (3), 423-450.
9. Luongo A (1992). Mode localization by structural imperfections in onedimensional continuous systems, J Sound Vib, 155 (2), 249-271.
10. Photiadis DM (1992), Anderson localization of one-dimensional wave propagation on a fluid-loaded plate, J Acoust Soc Am, 91 (2), 771-780.
11. Bouzit D and Pierre C (1993), “Localization of vibration in disordered multi-span beams with damping,” In Structural Dynamics of Large Scale and Complex Systems, ASME Pub DE-Vol 59, Proc 14th Biennial Conf on Mech Vib and Noise, Albuquerque NM, Sept 19-22.
12. Levine MB and Salama MA (1991), Experimental Investigation of the Mode Localization Phenomenon. JPL Report D-8767, Jet Propulsion Lab, Pasadena CA.
13. Rosenberg RM (1966), On nonlinear vibrations of systems with many degrees of freedom, Adv Appl Mech, 9, 155-242.
14. Kauderer H (1958), Nichtlineare Mechanik, Springer Verlag, Berlin and New York.
15. Rand RH (1971), A higher order approximation for nonlinear normal modes in two degree of freedom systems, Int J Nonlinear Mech, 6, 545-547.
16. Mikhlin YuV (1985), The joining of local expansions in the theory of nonlinear oscillations, Prikl Matem Mekhan, 49 (5), 738-743.
17. Vakakis AF (1990), Analysis and Identification of Linear and Nonlinear Normal Modes in Vibrating Systems, PhD Thesis, California Inst of Tech, Pasadena CA.
18. Shaw SW and Pierre C (1991). Nonlinear normal modes and invariant manifolds.,/Sound Vib, 150(1), 170-173.
19. King ME and Vakakis AF (1993b), An energy-based formulation for computing nonlinear normal modes in undamped continuous systems, J Vib Acoust, 116 (3), 332-340.
20. Happawana GS, Bajaj AK, and Azene M (1995), An analytical solution to nonsimilar normal modes in a strongly nonlinear discrete system, J Sound Vib, 183(2), 361-368.
21. King ME (1994), Analytical and Experimental Aspects of Nonlinear Normal Modes and Nonlinear Mode Localization, PhD Thesis, Univ of Illinois at Urbana - Champaign, Urbana IL.
22. Nayfeh AH and Chin C (1996), On nonlinear normal modes of systems with internal resonance, J Vib Acoust, (in press).
23. Vakakis AF and Rand RH (1992), Normal modes and global dynamics of a two degree of freedom nonlinear system: I low energies, and II high energies, Int J Nonlinear Mech, 27 (5), 861-888.
24. Vakakis AF and Cetinkaya, C (1993), Mode localization in a class of multi degree of freedom nonlinear systems with cyclic symmetry, SIAM J Appl Math, 53, 265-282.
25. Vakakis AF, Nayfeh TA, and King ME (1993), A multiple-scales analysis of nonlinear, localized modes in a cyclic periodic system, J Appl Mech, 60 (2), 388-397.
26. King ME and Vakakis AF (1994), Asymptotic analysis of nonlinear mode localization in a class of coupled continuous structures, Int J Solids Struct, 32 (8/9), 1161-1177.
27. Nayfeh AH (1995), On direct methods for constructing nonlinear normal modes of continuous systems, J Vib Control, 1, 477-481.
28. King ME and Vakakis AF (1995), A very complicated structure of resonances in a nonlinear system with cyclic symmetry, Nonlinear Dyn, 7, 85-104.
29. King ME and Vakakis AF (1995), Mode localization in a system of coupled flexible beams with geometric nonlinearities, ZAMM, 75 (2), 127-139.
30. Vakakis AF (1994), Passive spatial confinement of implusive responses in coupled nonlinear beams, AIAA J, 32 (9), 1902-1910.
31. Aubrecht J and Vakakis AF (1996), Localized and non-localized nonlinear normal modes in a multi-span beam with geometric nonlinearities, J Vib Acoust (in press).
32. Nayfeh AH and Mook D (1985). Nonlinear Oscillations, Wiley Interscience, New York.
33. Timoshenko S, Young DH, and Weaver W (1974) Vibration Problems in Engineering, John Wiley & Sons, New York.
34. Aubrecht J, Vakakis AF, Tsao T-C, and Bentsman J (1996), Experimental study of nonlinear transient motion confinement in a system of coupled beams, J Sound Vib, (n press).
35. King ME, Aubrecht J, and Vakakis AF (1995), Experimental study of steady-state localization in coupled beams with active nonlinearities, J Nonlinear Sci, 5(6), 485-502.
36. King ME and Vakakis AF (1994), A Method for Studying Waves with Spatially Localized Envelopes in a Class of Nonlinear Partial Differential Equations, Wave Motion, 19, 391-405.
37. Weinstein A (1985), Periodic nonlinear waves on a half-line, Commun Math Phys, 99, 385-388.
38. 4 -theory, Phys Rev Lett, 58, p. 747.
39. Vakakis AF, Manevitch LI, Milchlin YuV, Pilipchuk VN, and Zevin AA (1996), Normal Modes and Localization in Nonlinear Systems, Wiley Interscience, New York, (in press).