Wave localization in multi-coupled periodic structures: Application to truss beams

Applied Mechanics Reviews

Volumn 49, Issue 2, 1996, Pages 65-86

  Pierre, Christophe ^a   Castanier, Matthew P ^a   Chen, Wan Joe ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DYNAMIC RESPONSE; LYAPUNOV METHODS; MATRIX ALGEBRA; RANDOM PROCESSES; STRUCTURAL ANALYSIS; TRUSSES; WAVE TRANSMISSION;

DISORDERED PERIODIC STRUCTURES; LYAPUNOV EXPONENTS; MULTICOUPLED PERIODIC STRUCTURES; WAVE LOCALIZATION; WAVE TRANSFER MATRIX;

BEAMS AND GIRDERS;

EID: 0030079887     PISSN: 00036900     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.3101889     Document Type: Article

References (62)

1. Anderson PW (1958), Absence of diffusion in certain random lattices, Phys Rev 109(5) 1492-1505.
2. Ariaratnam ST and Xie WC (1991), “Lyapunov exponents in stochastic structural dynamics,” in Lyapunov exponents: Proc of a Conf in Oberwolfach, May 28-June 2, 1990, Springer-Verlag, New York, 271-291.
3. Ariaratnam ST and Xie WC (1992), “On the localization phenomenon in randomly disordered engineering structures,” in Nonlinear Stochastic Mechanics: IUTAM Symp, Turin, 1991, Springer-Verlag, New York, 13-24.
4. Bendiksen OO (1987), Mode localization phenomena in large space structures, AIAA J, 25(9) 1241-1248.
5. Bougerol P and Lacroix J (1985), Products of Random Matrices with Applications to Schrödinger Operators, Birkhauser Boston Inc, Boston.
6. Bouzit D (1993), Wave localization and conversion phenomena in disordered multi-span beams: Theory and experiment, PhD Dissertation, Univ of Michigan.
7. Bouzit D and Pierre C (1992), Vibration confinement phenomena in disordered, mono-coupled, multi-span beams, ASME Trans J Vib Acoust 114(4) 521-530.
8. Bouzit D and Pierre C (1993), “Wave localization and conversion phenomena in multi-coupled multi-span beams,” in Aerospace Structures: Nonlinear Dynamics and System Response, JP Cusumano et al (eds), ASME AD-Vol 33, New York, 67-83.
9. Bouzit D and Pierre C (1995), An experimental investigation of vibration localization in disordered multi-span beams, J Sound Vib 187(4), 649-669.
10. Brillouin L (1953), Wave Propagation in Periodic Structures, Dover, New York.
11. Cai GQ and Lin YK (1991), Localization of wave propagation in disordered periodic structures, AIAA 29(3) 450-456.
12. Castanier MP and Pierre C (1993), Individual and interactive mechanisms for localization and dissipation in a mono-coupled nearly-periodic structure, J Sound Vib 168(3) 479-505.
13. Castanier MP and Pierre C (1995), Lyapunov exponents and localizatioi phenomena in multi-coupled nearly-periodic systems, J Sound Vib 183 (3) 493-515.
14. Cha PD and Morganti CR (1994), Numerical statistical investigation on the dynamics of finitely long, nearly periodic chains, AIAA 32(11) 2269-2275.
15. Cha PD and Pierre C (1991), Vibration localization by disorder in assemblies of monocoupled, multimode component systems, ASME Trans j Appl Mech 58 1072-1081.
16. Chen WJ (1993), Vibration localization and wave conversion phenomena in a multi-coupled, nearly periodic, disordered truss beam, PhD Dissertation, Univ of Michigan.
17. Chen WJ and Pierre C (1991), “Exact linear dynamics of periodic and disordered truss beams: Localization of normal modes and harmonic waves,” in Proc of 32nd AIAA/ASME/ASCE/AHS/ASC Struct, Struct Dyn, and Mat Conf Baltimore MD, April 1991.
18. Chen WJ and Pierre C (1992), “Vibration localization and wave conversion phenomena in a multi-coupled, nearly periodic, disordered truss beam,” in Proc of 33rd AIAA/ASME/ASCE/AHS/ASC Struct, Struct Dyn, and Mat Conf, Dallas TX, April 1992.
19. Cornwell PJ and Bendiksen OO (1989), Localization of vibrations in large space reflectors, AIAA 27(2) 219-226.
20. Furstenberg H (1963), Noncommuting random products, Trans Am Math Soc 108(3) 377-428.
21. Happawana GS, Bajaj AK, and Nwokah ODI (1991), A singular perturbation perspective on mode localization J Sound Vib 147(2) 361-365.
22. Herbert DC and Jones R (1971), Localized states in disordered systems., J Phys C: Solid State Phys 4 1145-1161.
23. Hodges CH (1982), Confinement of vibration by structural irregularity, J Sound Vib 82(3) 411-424.
24. Hodges CH and Woodhouse J (1983), Vibration isolation from irregularity in a nearly periodic structure: theory and measurements, J Acoust Soc Am 74(3) 894-905.
25. Hodges CH and Woodhouse J (1986), Theories of noise and vibration transmission in complex structures Reports Prog Phys 49 107-170.
26. Hodges CH and Woodhouse J (1989a), Confinement of vibration by onedimensional disorder, I: Theory of ensemble averaging, J Sound Vib 130(2) 237-251.
27. Hodges CH and Woodhouse J (1989b), Confinement of vibration by onedimensional disorder, II: A numerical experiment on different ensemble averages, J Sound Vib 130(2) 253-268.
28. Ibrahim RA (1987), Structural dynamics with parameter uncertainties, Appl Mech Rev 40(3) 309-328.
29. Ishii K (1973), Localization of eigenstates and transport phenomena in the one-dimensional disordered system, Suppl of Prog Theor Phys 53 77138.
30. Kissel GJ (1988), Localization in disordered periodic structures, PhD Dissertation, Massachusetts Inst of Tech.
31. Kissel GJ (1991), Localization factor for multichannel disordered systems, Phys Rev A 44(2) 1008-1014.
32. Lee U (1990), Dynamic continuum modeling of beamlike space structures using finite element matrices, AIAA 28(4) 725-731.
33. Levine-West MB and Salama MA (1992), “Mode localization experiments on a ribbed antenna,” in Proc of 33rd AIAA/ASME/ASCE/AHS/ASC Struct, Struct Dyn, and Mat Conf Dallas TX, April 1992, 2038-2047.
34. Li D and Benayora H (1992), Dynamics of periodic and near-periodic structures, Appl Mech Rev 45(11) 447-459.
35. Lust SD, Friedmann PP, and Bendiksen OO (1991), “Free and forced response of nearly periodic multi-span beams and multi-bay trusses,” in Proc of 32nd AIAA/ASME/ASCE/AHS/ASC Struct, Structural Dyn, and Mat Conf, Baltimore MD, April 1991, 2831-2842.
36. Matsuda H and Ishii K (1970), Localization of normal modes and energy transport in the disordered harmonic chain, Suppl of Prog Theor Phys 45 56-86.
37. Mead DJ (1975a), Wave propagation and natural modes in periodic systems, I: monocoupled systems, J Sound Vib 49(1) 1-18.
38. Mead DJ (1975b), Wave propagation and natural modes in periodic systems, II: multi-coupled systems, with and without damping J Sound Vib 49(1) 19-39.
39. Miller DW and von Flotow AH (1989), A traveling wave approach to power flow in structural networks, J Sound Vib 128 145-162.
40. Mills RA (1985), Natural vibrations of beam-like trusses, SM Thesis, Massachusetts Inst of Tech.
41. Necib B and Sun CT (1989), Analysis of truss beams using a high order Timoshenko beam finite element, J Sound Vib 130 149-159.
42. Noor AK (1988), Continuum modeling for repetitive lattice structures, Appl Mech Rev 41(7) 285-296.
43. Orgun CO and Tongue BH (1994), Mode localization in coupled circular plates, ASME Trans J Vib Acoust 116 286-294.
44. Oseledec VI (1968), A multiplicative ergotic Theorem: Ljapunov characteristic numbers for dynamical systems, Trans Moscow Math Soc 19 197-231.
45. Ottarsson GS and Pierre C (1995), A transfer matrix approach to free vibration localization in mistuned blade assemblies, J Sound Vib, Accepted for publication.
46. Photiadis DM (1993), “Localization of helical flexural waves on an irregular cylindrical shell,” in Structural Dynamics of Large Scale and Complex Systems, C Pierre and NC Perkins (eds), ASME DE-Vol 59, New York, 15-26.
47. Pierre C (1988), Mode localization and eigenvalue loci veering phenomena in disordered structures, J Sound Vib 126(3) 485-502.
48. Pierre C (1990), Weak and strong vibration localization in disordered structures: a statistical investigation, J Sound Vib 139(1) 111-132.
49. Pierre C and Cha PD (1989), Strong mode localization in nearly periodic disordered structures, AIAA 27(2) 227-241.
50. Pierre C and Dowell EH (1987), Localization of vibrations by structural irregularity, J Sound Vib 114 549-564.
51. Pierre C and Murthy DV (1992), Aeroelastic modal characteristics of mistuned blade assemblies: Mode localization and loss of eigenstructure, AIAA 30(10) 2483-2496.
52. Pierre C, Tang DM, and Dowell EH (1987), Localized vibrations of disordered multispan beams: Theory and experiment, AIAA 25(9) 1249-1257.
53. Scott JFM (1985), The statistics of waves propagating in a one-dimensional random medium, Proc of Royal Soc of London A398 341-363.
54. Signorelli J and von Flotow AH (1988), Wave propagation, power flow, and resonance in a truss beam, J Sound Vib 126 127-144.
55. Thouless DJ (1972), A relation between the density of states and range of localization for one dimensional random systems, J Phys C: Solid State Phys 5 77-81.
56. Vakakis AF and Cetinkaya C (1993), Mode localization in a class of multidegree of freedom nonlinear systems with cyclic symmetry, SIAM J Appl Math 53 265-282.
57. Vakakis AF, Nayfeh T, and King M (1993), A multiple-scales analysis of nonlinear localized modes in a cyclic periodic system, ASME Trans J Appl Mech 60 849-856.
58. von Flotow AH (1986), Disturbance propagation in structural networks, J Sound Vib 106(3) 433-450.
59. Wolf A, Swift JB, Swinney HL, and Vastano JA (1985), Determining Lyapunov exponents from a time series, Physica D 16 285-317.
60. Yong Y and Lin YK (1989), Propagation of decaying waves in periodic and piecewise periodic structures of finite length, J Sound Vib 129 99118.
61. Yong Y and Lin YK (1990), Dynamics of complex truss-type space structures, AIAA 28(7) 1250-1258.
62. Ziman JM (1979), Models of Disorder, Cambridge Univ Press, Cambridge, England.