Modal Analysis of Bridge Structures:

Mohamed Abdel-Ghaffar Symposium at USC September 19, 2008 Modal Analysis of Bridge Structures: An Application to Noise Generation from Modular Expans...
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Mohamed Abdel-Ghaffar Symposium at USC September 19, 2008

Modal Analysis of Bridge Structures: An Application to Noise Generation from Modular Expansion Joint

Hiroki Yamaguchi Saitama University

1

MEMORY OF PROF. ABDEL-GHAFFAR

International Seminar on CableSupported Bridges, Yokohama, Japan, December 10,1991. 2

Impact of Prof. Abdel‐Ghaffar’s Work http://stevens.usc.edu/read_article.php?news_id=282

Ahmed M. Abdel-Ghaffar, an internationally known USC civil engineering professor specializing in the analysis and monitoring long span flexible bridges, died April 17 after a long illness. Abdel-Ghaffar’s 1974 investigation of the dynamic characteristics of the Vincent Thomas Bridge in Los Angeles, done when he was a graduate student, led to new standards on how to collect, analyze and interpret structural dynamic measurements from complex, three-dimensional, extended structures. Experimental and Theoretical Modal Analysis of Bridge Structures: An Application to Noise Generation from Modular Expansion Joint 3

BACKGROUND Modular Expansion Joint

Middle Beam Rubber Sealing

 Large expansion capacity in both translation and rotation  Drainage of water and debris with the use of rubber sealing DRAWBACK: Louder noise is generated and radiated when the vehicle crosses the joint and this has been a localized environmental problem. 4

OBJECTIVES Input-Output System Diagram of Joint Noise Problem

Car Running

Joint Structure Cavity

Structure Vibration

Bridge Structure Cavity

Air Vibration

Transfer Characteristics Natural freq. & mode of joint structure Acoustic freq. & mode of sealing gap

Air

Transfer Characteristics Mass Additio n Gap Filling

Sound Receiving Point

Human

Response

Noise

Transfer Characteristics

Annoyance ・Frequency Domain ・Time Domain

Sound Barrier

Noise Control

 Mechanism of noise generation from modular joint in highway bridges 5

Car-Running Experiment with Full-Scale Model of Modular Joint

6

FULL-SCALE MODEL OF JOINT

Sedan-Type Two-Axle Car Car Speed: 50 km/h

Sound Level Meter 7

TIME SERIES OF SOUND & VIBRATION

Sound below the joint

Sound above the joint

Lateral acceleration The Fourier spectrum was obtained by scanning a Hanning window of length 0.4096sec over the first 0.6sec record.

Vertical acceleration 8

SPECTRA OF SOUND PRESSURE

Car running over the control beams

Car running over the support beams

Above the joint

Below the joint

9

MECHANISM OF NOISE ABOVE JOINT

Acoustic characteristics of gap

10

MECHANISM OF NOISE BELOW JOINT Acoustic characteristics of test cavity

Dynamic characteristics of joint

11

DYNAMIC CHARACTERISTICS OF JOINT

Impact testing

FEM analysis 12

NATURAL FREQ. & MODE SHAPE

Lateral vibration mode

Vertical vibration mode 13

VIBRO-ACOUSTIC ANALYSIS BY FEM 1. Dominant contribution from structural mode

f = 161 Hz

f = 160 Hz

f = 162 Hz

2. Significant contribution from structural and acoustic modes f = 267 Hz

f = 268 Hz (a)

(b)

f = 269 Hz (c)

14

POSSIBLE SOURCES OF NOISE GENERATION

Rubber sealing

Gap

Deck

Deck Support beam cavity Girder

Girder Structural-acoustic interaction

Pier 15

Field Measurement of Noise Generated from Modular Expansion Joint in Highway Bridges

16

FIELD MEASUREMENT: STEEL BRIDGE Expansion joint Concrete deck slab

Cavity below the joint Cavity below the joint

Steel I-girder

Expansion joint

THE HACCHOME BRIDGE  Bridge length of 184.6m with 5 continuous spans  Non-composite, four steel I-girder with concrete deck slab  Modular joint for the new bridge  Finger joint for the old bridge with five I-girder 17

POSITION OF NOISE METERS Above the bridge Expansion joint

6m

Bridge abutment

5m

Bridge side

Just below the joint 5m

Under the girder 18

POSITION OF ACCELEROMETERS

Middle beam of joint

Concrete deck slab

Web plate of I-girder

ÉW ÉC Éá Éìïž Ég ñ ê} ÉW

ÉC á

Ég ì

ï ž ñ

ê}

19

TIME SERIES OF VIBRATIONS & SOUND

Joint Vibration

Girder’s Web Vibration

Slab Vibration

Sound under Girder 20

Vibration of Girder Web

Frequency (Hz)

Vibration of Joint

Frequency (Hz)

Sound under Bridge

Sound Pressure Frequency (Hz) (Pa)

TIME-FREQ. PLOT OF SOUND UNDER BRIDGE

(WTC)

Time (s)

Time (s)

3621

Sound Pressure (Pa)

TIME-FREQ. PLOT OF SOUND ABOVE BRIDGE

Frequency (Hz)

(WTC)

Acceleration

(m/s2)

Time (s)

Time (s)

Joint Vibration 22

FIELD MEASUREMENT: CONCRETE BRIDGE Expansion joint

Concrete box-girder

Cavity below the joint

Expansion joint

THE UTSUKUSHIMA BRIDGE  Bridge length of 208m with 3 continuous spans  PC box-girder  Modular joint with five middle beams 23

POSITION OF NOISE METERS

Just below the joint

Bridge side

Under the girder

Above the bridge Cavity below the joint

2.62m

Just below the joint Bridge Pier

Under the girder

7m 5m

10m Bridge side 24

POSITION OF ACCELEROMETERS

Support beam of joint

Upper slab of box-girder

20m Box-girder

Approach

Middle beam of joint

7.35m

5m

Expansion joint

25

TIME SERIES OF VIBRATION & SOUND

Joint Vibration

Sound below Joint

Sound under Girder

Sound above Bridge

Sound beside Bridge 5m

Sound beside Bridge 15m 26

5

5

Joint Vibration

2

Joint Vibration

Acceleration â¡ë¨ìx[m/s (m/s ] 2)

2 Acceleration â¡ë¨ìx[m/s ](m/s2)

TIME-FREQ. PLOT OF SOUND IN PC BRIDGE

0

0

-5

-5 0

0.1

0.2

0.3 éû ä‘ [s ]

0.4

0.5

0.6

0

0.1

0.2

Sound below Joint

900

900

800

800

700

700

600 500 400 300 200

0.5

0.6

600 500 400 300 200 100

100 0

0.4

Sound above Bridge

1000

Acceleration (m/s2)

Acceleration (m/s2)

1000

0.3 éû ä‘ [s ] Time (s)

Time (s)

0.1

0.2

0.3

Time (s)

0.4

0.5

0.6

0

0.1

0.2

0.3

0.4

0.5

0.6

Time (s)

(3) 700-800Hz: non-stationary component (2) 400-600Hz due to Joint Cavity Sound due to Sealing Gap Sound (1) 100-200Hz: main, stationary component due to Joint Vibration 27

CONCLUDING REMARKS  The noise generated above the joint is dominated by frequency components in the frequency range from 500 to 800 Hz, which is attributed to a sudden change in the air pressure within the gap formed by the rubber sealing with the two adjacent middle beams when a car runs over the gap.  The noise generated below the joint is mainly dominated by the frequency components in the frequency range below 200 Hz, which is caused by the sound radiation due to the bending vibration modes of the middle beams being excited by an impact force from the car wheels.  The noise generated below the joint can be significantly affected by the acoustic characteristics of the cavity below the joint in the sense that there is a possibility of acoustic resonance in the space.  The sound radiation efficiency of the joint-cavity system appeared to be high at natural frequencies of vibration modes of the joint with significant vertical vibration of middle and support beams.

28

OUTLINE Modal Analysis of Bridge Structures: An Application to Noise Generation from Modular Expansion Joint

• Background • Objectives • Car-Running Experiment with Full-Scale Model of Modular Expansion Joint – Experimental Modal Analysis of Model Joint and Cavity – Theoretical Modal Analysis of Model Joint and Cavity

• Field Measurement of Noise Generated from Modular Expansion Joint in Highway Bridges • Concluding Remarks 29

NOISE UNDER THE BRIDGE Finger Joint Sound pressure (Pa)

Sound pressure (Pa)

Modular Joint

Sound pressure (Pa)

Frequency (Hz)

Frequency (Hz)

Truck

Frequency (Hz)

Dominant in low freq. region

モジュラー型ジョイント通 過によるジョイント音の影 響 30

NOISE ABOVE THE BRIDGE Finger Joint Sound pressure (Pa)

Sound pressure (Pa)

Modular Joint

Frequency (Hz)

Frequency (Hz)

Sound pressure (Pa)

トラッ ク

Dominant in high freq. region

モジュラー型ジョイント特 有の空間圧縮音の影響 Frequency (Hz)

31