In this study, a model for the analysis of the wave localization in a special kind of simply-supported beam bridge, namely, the periodic elevated railway (PER), is developed. For simplicity, each span of the PER is supposed to be composed of two longitudinal beams, a pier, and three linking springs. The standard linear solid model is employed to describe the damping of the materials of the piers and beams. Transfer matrix for each span of the PER undergoing in-plane vibration is derived, whereby the wave transfer matrix for each span is obtained. By means of the Wolf's algorithm and using the aforementioned wave transfer matrices, the localization factors accounting for wave localization in the PER are determined. With the proposed model, the influence of the disorder of the beam lengths on the wave localization in the PER is examined. Also, the interactive effect of the damping and the beam-length disorder on the wave localization in the PER is investigated. As a special case, the wave localization in a PER with rigid beam-beam-pier (BBP) junctions is also discussed in this study. Moreover, by the wave transfer matrix method, the wave localization and conversion phenomena in a finite disordered PER segment are investigated. Finally, the relation between the response of a finite disordered PER segment to external loadings and the degrees of the disorder of the PER segment is examined.

References

References
1.
Hodges
,
C. H.
,
1982
, “
Confinement of Vibration by Structure Irregularity
,”
J. Sound Vib.
,
82
, pp.
411
424
.10.1016/S0022-460X(82)80022-9
2.
Hodges
,
C. H.
, and
Woodhouse
,
J.
,
1989
, “
Confinement of Vibration by One-Dimensional Disorder, I: Theory of Ensemble Averaging
,”
J. Sound Vib.
,
130
(
2
), pp.
237
251
.10.1016/0022-460X(89)90552-X
3.
Mead
,
D. J.
,
1970
, “
Free Wave Propagation in Periodically Supported, Infinite Beams
,”
J. Sound Vib.
,
11
, pp.
181
197
.10.1016/S0022-460X(70)80062-1
4.
Mead
,
D. J.
,
1973
, “
A General Theory of Harmonic Wave Propagation in Linear Periodic Systems With Multiple Coupling
,”
J. Sound Vib.
,
27
, pp.
235
260
.10.1016/0022-460X(73)90064-3
5.
Mead
,
D. J.
,
1975
, “
Wave Propagation and Natural Modes in Periodic Systems: I. Mono-Coupled Systems
,”
J. Sound Vib.
,
40
, pp.
1
18
.10.1016/S0022-460X(75)80227-6
6.
Mead
,
D. J.
,
1975
, “
Wave Propagation and Natural Modes in Periodic Systems: II. Multi-Coupled Systems, With and Without Damping
,”
J. Sound Vib.
,
40
, pp.
19
39
.10.1016/S0022-460X(75)80228-8
7.
Pierre
,
C.
, and
Bouzit
,
D.
,
1992
, “
Vibration Confinement Phenomena in Disordered, Mono-Coupled, Multi-Span Beams
,”
ASME J. Vibr. Acoust.
,
114
, pp.
521
530
.10.1115/1.2930294
8.
Pierre
,
C.
, and
Dowell
,
E. H.
,
1987
, “
Localization of Vibrations by Structural Irregularity
,”
J. Sound Vib.
,
114
, pp.
549
564
.10.1016/S0022-460X(87)80023-8
9.
Kissel
,
G. J.
,
1991
, “
Localization Factor for Multichannel Disordered Systems
,”
Phys. Rev. A
,
44
, pp.
1008
1014
.10.1103/PhysRevA.44.1008
10.
Chen
,
W. J.
, and
Pierre
,
C.
,
1992
, “
Vibration Localization and Wave Conversion Phenomenon in a Multi-Coupled, Nearly Periodic, Disordered Truss Beam
,”
AIAA
Paper No. 92-2115.10.2514/6.1992-2115
11.
Bouzit
,
D.
, and
Pierre
,
C.
,
2000
, “
Wave Localization and Conversion Phenomenon in Multi-Coupled Multi-Span Beams
,”
Chaos, Solitons Fractals
,
11
, pp.
1575
1596
.10.1016/S0960-0779(99)00079-X
12.
Cai
,
G. Q.
, and
Lin
,
L. Y.
,
1991
, “
Localization of Wave Propagation in Disordered Periodic Structures
,”
AIAA J.
,
29
, pp.
345
349
.10.2514/3.10599
13.
Li
,
D.
, and
Benaroya
,
H.
,
1996
, “
Vibration Localization in Multi-Coupled and Multi-Dimensional Near-Periodic Structures
,”
Wave Motion
,
23
, pp.
67
82
.10.1016/0165-2125(95)00045-3
14.
Castanier
,
M. P.
, and
Pierre
,
C.
,
1993
, “
Individual and Interactive Mechanisms for Localization and Dissipation in Mono-Coupled Nearly-Periodic Structure
,”
J. Sound Vib.
,
168
, pp.
479
505
.10.1006/jsvi.1993.1387
15.
Lust
,
S. D.
,
Friedmann
,
P. P.
, and
Bendiksen
,
O. O.
,
1990
, “
Mode Localization in Multi-Span Beams
,”
Proceedings of the AIAA Dynamics Specialists Conference
, Long Beach, CA, April 5–6,
AIAA
Paper No. 90-1214, pp.
225
235
.10.2514/6.1990-1214
16.
Bouzit
,
D.
, and
Pierre
,
C.
,
1995
, “
Localization of Vibration in Disordered Multi-Span Beams With Damping
,”
J. Sound Vib.
,
187
, pp.
625
648
.10.1006/jsvi.1995.0549
17.
Fu
,
Q. X.
,
Zhong
,
L.
, and
Lu
,
J. F.
,
2013
, “
Wave Localization in a Disordered Periodic Viaduct Undergoing Out-of-Plane Vibration
,”
Arch. Appl. Mech.
(in press).10.1007/s00419-013-0734-9
18.
Graff
,
K. F.
,
1991
,
Wave Motion in Elastic Solids
,
Dover
,
New York
.
19.
Carcione
,
J.
,
2001
,
Wave Fields in Real Media-Wave Propagation in Anisotropic, Anelastic and Porous Media
,
Pergamon
,
New York
.
20.
Kittel
,
C.
,
1996
,
Introduction to Solid State Physics
,
Wiley
,
New York
.
21.
Kennett
,
B. L. N.
,
1983
,
Seismic Wave Propagation in Stratified Media
,
Cambridge University
,
New York
.
22.
Wolf
,
A.
,
Swift
,
J. B.
,
Swinney
,
H. L.
, and
Vastano
,
J. A.
,
1985
, “
Determining Lyapunov Exponents From a Time Series
,”
Physica D
,
16
, pp.
285
317
.10.1016/0167-2789(85)90011-9
23.
Castanier
,
M. P.
, and
Pierre
,
C.
,
1995
, “
Lyapunov Exponents and Localization Phenomena in Multi-Coupled Nearly Periodic Systems
,”
J. Sound Vib.
,
183
, pp.
493
515
.10.1006/jsvi.1995.0267
24.
Chen
,
A. L.
,
Li
,
F. M.
, and
Wang
,
Y. S.
,
2007
, “
Localization of Flexural Waves in a Disordered Periodic Piezoelectric Beam
,”
J. Sound Vib.
,
304
, pp.
863
874
.10.1016/j.jsv.2007.03.047
25.
Chen
,
Y.
, and
Li
,
C.
,
2000
, “
Dynamic Response of Elevated High-Speed Railway
,”
J. Bridge Eng.
,
5
, pp.
124
130
.10.1061/(ASCE)1084-0702(2000)5:2(124)
26.
Majka
,
M.
, and
Hartnett
,
M.
,
2008
, “
Effects of Speed, Load and Damping on the Dynamic Response of Railway Bridges and Vehicles
,”
Comput. Struct.
,
86
, pp.
556
572
.10.1016/j.compstruc.2007.05.002
27.
Ju
,
S. H.
,
2002
, “
Finite Element Analyses of Wave Propagations Due to a High-Speed Train Across Bridges
,”
Int. J. Numer. Methods Eng.
,
54
, pp.
1391
1408
.10.1002/nme.473
28.
Wu
,
Y. S.
, and
Yang
,
Y. B.
,
2004
, “
A Semi-Analytical Approach for Analyzing Ground Vibrations Caused by Trains Moving Over Elevated Bridges
,”
Soil Dyn. Earthquake Eng.
,
24
, pp.
949
962
.10.1016/j.soildyn.2004.06.020
You do not currently have access to this content.