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Research Papers

Vibration and Acoustic Analysis of Trussed Railroad Bridge Under Moving Loads

[+] Author and Article Information
R. Daniel Costley

Engineer Research and Development Center,
U.S. Army of Corps of Engineers,
3909 Halls Ferry Road,
CEERD-GS-S 5014,
Vicksburg, MS 39180-6199
e-mail: dan.costley@usace.army.mil

Henry Diaz-Alvarez

Engineer Research and Development Center,
U.S. Army of Corps of Engineers,
3909 Halls Ferry Road,
CEERD-GS-S 5014,
Vicksburg, MS 39180-6199
e-mail: henry.diaz-alvarez@usace.army.mil

Mihan H. McKenna

Engineer Research and Development Center,
U.S. Army of Corps of Engineers,
3909 Halls Ferry Road,
CEERD-GS-S 5014,
Vicksburg, MS 39180-6199
e-mail: mihan.h.mckenna@usace.army.mil

Anna M. Jordan

Mem. ASME
Engineer Research and Development Center,
U.S. Army of Corps of Engineers,
3909 Halls Ferry Road,
CEERD-GS-S 5014,
Vicksburg, MS 39180-6199
e-mail: anna.m.jordan@usace.army.mil

1Corresponding author.

Contributed by the Noise Control and Acoustics Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received March 12, 2014; final manuscript received November 18, 2014; published online January 27, 2015. Assoc. Editor: Liang-Wu Cai.

This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States. Approved for public release; distribution is unlimited.

J. Vib. Acoust 137(3), 031009 (Jun 01, 2015) (10 pages) Paper No: VIB-14-1075; doi: 10.1115/1.4029213 History: Received March 12, 2014; Revised November 18, 2014; Online January 27, 2015

A finite element (FE) model was developed for a Pratt truss railroad bridge located at Ft. Leonard Wood, MO. This model was used to investigate the vibration responses of a bridge under vehicle loading. Modeling results were obtained for a single axle with two wheels traversing the bridge at different speeds. The current model does not include the effects of vehicle suspension. Superposition of multiple axles was used to represent a locomotive transiting the bridge. The output of the vibration response was used as an input to an acoustic FE model to determine which vibrational modes radiate infrasound. The vibration and acoustic models of the railroad bridge will be reviewed, and results from the analysis will be presented. Measurements from an accelerometer mounted on the bridge agree reasonably well with model results. Infrasound could potentially be used to remotely provide information on the capacity and number of vehicles traversing the bridge and to monitor the bridge for significant structural damage.

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References

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Imaichi, K., Tsujimoto, Y., and Takabatake, S., 1982, “Theoretical Analysis of Infrasound Radiation From an Oscillating Bridge,” J. Sound Vib., 81(4), pp. 453–468. [CrossRef]
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Fryba, L., 1972, Vibration of Solids and Structures Under Moving Loads, Noordhoff International Publishing, Groningen, The Netherlands.
Chattrrjee, P. K., Datta, T. K., and Surana, C. S., 1993, “Dynamic Response of Trussed Bridges for Moving Loads,” Comput. Struct., 46(6), pp. 1085–1093. [CrossRef]
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Ju, S.-H., and Lin, H.-T., 2008, “Experimentally Investigating Finite Element Accuracy for Ground Vibrations Induced by High-Speed Trains,” Eng. Struct., 30(3), pp. 733–746. [CrossRef]
Diaz-Alvarez, H., McKenna, M. H., and Mlakar, P. F., 2009, “Infrasound Assessment of Infrastructure; Report 1: Field Testing and Finite Element Analysis for Railroad Bridge A.B. 0.3, Fort Leonard Wood, Missouri,” U.S. Army Engineer Research and Development Center, Vicksburg, MS, Report No. ERDC/GSL TR-09-16.
Koppenhoefer, K., Yushanov, S., and McKenna, M. H., 2010, “Infrasound Assessment of Infrastructure; Report 3: Numerical Simulation of Structural–Acoustic Coupling and Infrasonic Propagation Modeling for Railroad Bridge A.B. 0.3, Fort Leonard Wood, Missouri,” U.S. Army Engineer Research and Development Center, Vicksburg, MS, Report No. ERDC/GSL TR-09-16.
McKenna, M. H., Yushanov, S., Koppenhoefer, K., and McKenna, J., 2009, “Analysis of the Acoustic Response of a Railroad Bridge,” COMSOL Conference, Boston, MA, Oct. 8–10.
Costley, R. D., Diaz-Alvarez, H., and McKenna, H. M., 2012, “Infrasound Assessment of Infrastructure; Report 5: Vibration and Acoustic Analysis of Railroad Bridge A.B. 0.3, Fort Leonard Wood, Missouri,” U.S. Army Engineer Research and Development Center, Vicksburg, MS, Report No. ERDC/GSL TR-09-16.
Costley, R. D., Diaz-Alvarez, H., and McKenna, H. M., 2012, “Vibrational and Acoustical Analysis of Trussed Railroad Bridge Under Moving Loads,” ASME Paper No. NCAD2012-1490. [CrossRef]
Costley, R. D., Diaz-Alvarez, H., and McKenna, M. H., 2011, “Structural Acoustic Analysis of a Railroad Bridge,” 2011 Military Sensing Symposia—Battlespace Acoustic, Magnetic, and Electric-Field Sensing and Signatures (BAMS), SENSIAC, Washington, DC, Oct. 24–27.
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Figures

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Fig. 1

Top—view of bridge from Little Piney River; bottom—schematic of geometry of bridge showing skewed ends, crossties, rails, and part of walkway

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Fig. 2

The load distribution function at a specific time

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Fig. 3

Top: vertical displacement (y-component) versus time of single point near middle of bridge. Bottom: vertical acceleration of same point.

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Fig. 4

Top: lateral displacement (z-component) versus time of single point near middle of bridge. Bottom: lateral acceleration of same point.

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Fig. 5

Power spectra of the vertical and lateral velocity of a point near the center of the bridge: from the top—1 axle traveling at 4.5 m/s; 1 axle traveling at 7 m/s; and 1 axle traveling at 9 m/s

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Fig. 6

Spectrogram for the vertical velocity of the point near the middle of the bridge for the case of a single axle traveling across the bridge at 4.5 m/s. The color bar at top is 10 × log10(V), where V represents the power spectral density of the velocity signal in units of (m/s)2/Hz.

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Fig. 7

Each curve represents the vertical particle accelerations of points along each of the stringers within the 8 Hz bin (7–10 Hz)

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Fig. 8

Each curve represents the envelope of the filtered signals from Fig. 7

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Fig. 9

Vertical acceleration profiles from the 8 Hz bin and 0.5–1.5 s interval for the case of a single axle traveling at 4.5 m/s: top—magnitude; bottom—phase

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Fig. 10

Particle acceleration versus time of the point near the middle of the bridge—top: vertical acceleration (y-component); bottom: lateral acceleration (z-component)

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Fig. 11

Power spectra of the vertical and lateral velocity of the point near the center of the bridge for a four axle locomotive traveling at 4.5 m/s

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Fig. 12

Spectrogram for the vertical velocity of the point near the middle of the bridge for a four axle locomotive traveling across the bridge at 4.5 m/s; the color bar is the same as in Fig. 6

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Fig. 13

Vertical acceleration profiles from the 8.5 Hz bin and 1–1.5 s interval for the case of a four axle locomotive traveling at 4.5 m/s—top: magnitude; bottom: phase

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Fig. 14

Comparison of accelerometer measurements with FE results

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Fig. 15

Schematic of bridge used in acoustic radiation model

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Fig. 16

SPL contours from the 8.5 Hz bin and 1–1.5 s interval for the case of a four axle locomotive traveling at 4.5 m/s—top: horizontal slice through the plane of the bridge; middle: vertical slice perpendicular to the axis of the bridge; bottom: vertical slice parallel to the length of the bridge

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Fig. 17

Total acoustic power radiated and the SPL at a point 90 m above the center of the bridge

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