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Research Papers

Dynamic Responses of a Four-Span Continuous Plate Structure Subjected to Moving Cars With Time-Varying Speeds

[+] Author and Article Information
Jing Yang

School of Engineering,
University of Liverpool,
Liverpool L69 3GH, UK
e-mail: jingyang06@csu.edu.cn

Huajiang Ouyang

School of Engineering,
University of Liverpool,
Liverpool L69 3GH, UK
e-mail: H.Ouyang@liverpool.ac.uk

Dan Stancioiu

Mechanical Engineering and Materials
Research Centre,
Liverpool John Moores University,
Liverpool L3 3AF, UK

Shancheng Cao

School of Engineering,
University of Liverpool,
Liverpool L69 3GH, UK
e-mail: shancheng.cao@polyu.edu.hk

Xuhui He

School of Civil Engineering,
Central South University,
Changsha 410075, China;
Joint International Research Laboratory of Key
Technology for Rail Traffic Safety,
Changsha 410075, China

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received September 4, 2017; final manuscript received February 17, 2018; published online May 7, 2018. Assoc. Editor: Izhak Bucher.

J. Vib. Acoust 140(6), 061002 (May 07, 2018) (15 pages) Paper No: VIB-17-1402; doi: 10.1115/1.4039799 History: Received September 04, 2017; Revised February 17, 2018

This paper presents an experimental and theoretical study of vibration of a four-span continuous plate with two rails on top and four extra supports excited by one or two moving model cars, which is meant to represent vehicle–track–bridge dynamic interaction. Measured natural frequencies of the plate structure are used to update the finite element (FE) model of the structure. Four laser displacement transducers are placed on the ground to measure the displacements of the plate. A laser-Doppler vibrometer is used to measure the real-time speed of the moving cars, which reveals that the speeds decrease with time at a small and almost constant deceleration which can affect the structural dynamic response. A fascinating experiment is the use of two cars connected in series, which is very rare and has never been done on a multispan structure. Vibration of the plate structure excited by two moving cars separated at a distance is also measured and exhibits interesting dynamic behavior too. A theoretical model of the whole structure is constructed and an iterative method is developed to determine the dynamic response. The numerical and the experimental results are found to agree very well, in particular when deceleration is considered in the theoretical model.

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Figures

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Fig. 3

Theoretical model of two cars: (a) elevation view of the first car, (b) cross section view of the first car, (c) elevation view of the second car, and (d) cross section view of the second car

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Fig. 4

Measured car speed: (a) raw data and picked points and (b) picked data and linearly fitted line in test 1

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Fig. 5

Displacements of plate at measured points by simulation considering acceleration of car (simulation 1) and results by simulation using average velocity of car (simulation 2) compared with experimental results for test 1

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Fig. 6

Spectrum of displacement of the plate structure at first measured point: (a) and (b) car–plate frequencies, (c) and (d) excited structural frequencies in free vibration after the car exits the plate structure, for test 1

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Fig. 7

Displacements of plate at measured points by simulation considering acceleration of car compared with experimental results for test 2

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Fig. 8

Spectrum of experimental displacement of the plate structure at first measured point: (a) car-excited response and (b) free vibration, for test 2

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Fig. 2

Schematic of the whole experimental setup from lateral view (unit: cm)

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Fig. 1

Pictures of experimental setup: (a) the second span of the four-span plate structure and (b) the side view of the two connected cars

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Fig. 9

Measured speeds of moving cars: (a) car 1 and (b) car 2, with linear fitting curves for test 3

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Fig. 10

Displacements of the plate at measured points by simulation compared with experimental results (red curve) for two separate moving cars with short time gap for test 3

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Fig. 11

Spectrum of experimental displacement of the plate structure at first measured point: (a) car-excited response and (b) free vibration, for test 3

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Fig. 18

Speed ratios where contact loss begins to happen for two types of car models

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Fig. 16

Displacements of measured points by simulation compared with experimental results for two connected moving cars for test 6

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Fig. 17

Spectrum of experimental displacement of the plate structure at first measured point: (a) dynamic response and (b) free vibration, for test 6

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Fig. 22

DAF versus initial speed ratio with mass ratio of 0.35 for different accelerations by two-connected car model: (a) DAF at first midspan, (b) DAF at second midspan, (c) DAF at third midspan, and (d) DAF at fourth midspan

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Fig. 19

DAF versus speed ratio for different mass ratios by two-connected-car model (“rm” representing mass ratio): (a) DAF at first midspan, (b) DAF at second midspan, (c) DAF at third midspan, and (d) DAF at fourth midspan

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Fig. 20

Spectra of numerical displacement of the plate structure at first measured point for mass ratios of: (a) 0.05, (b) 0.1, (c) 0.25, and (d) 0.35 by two-connected car model at speed ratio of 0.073

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Fig. 12

Displacements of the plate at measured points by simulation compared with experimental results for two separate moving cars with long time gap for test 4

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Fig. 21

Spectra of numerical displacement of the plate structure at first measured point for mass ratios of: (a) 0.05, (b) 0.1, (c) 0.25, and (d) 0.35 by moving mass model at speed ratio of 0.073

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Fig. 13

The speed of two connected cars measured by Laser Vibrometer and its linear fitting for test 5

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Fig. 14

Displacements of the plate at measured points by simulation compared with experimental results for two connected moving cars for test 5

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Fig. 15

Spectrum of experimental displacement of the plate structure at first measured point: (a) dynamic response and (b) free vibration, for test 5

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