The Twenty-Sixth KKHTCNN Symposium on Civil Engineering
November 18-20, 2013, Singapore

Errors on bridge vibration data measured by a passing vehicle
Kyosuke YAMAMOTO 1, Yuta NAKAGAMA2
Department of Engineering Mechanics and Energy, University of Tsukuba,
1-1-1 Ten-No-Dai, Tsukuba 3058573
yamamoto_k@kz.tsukuba.ac.jp; s1011192@u.tsukuba.ac.jp

ABSTRACTThis study presents the numerical simulation of VBI (Vehicle-Bridge Interaction) system andcompares the bridge and vehicle vibration responses. According to the numerical simulation,
bridge frequency tends to be around the natural frequency, regardless of the road profile. On
the other hand, the vehicle frequency is dominantly affected by the road profile, and tends tobe different from the bridge one.
BACKGROUNDVRA (Vehicle Response Analysis) technology for bridge damage detection is intensively
studied. In VRA, sensors are not installed on the bridge, but on a vehicle passing through themonitored bridge, and the bridge damage is estimated by using the vibration data of the vehicle.
This technology is inspired by “Indirect Approach”, which was proposed by Yang et al., in2004, and it has been improved by many researchers. In SHM (Structure Health Monitoring)
methods using vibration, structural damages are generally estimated by changes of vibration
characteristics. Thus, in VRA, the measured vibrations of a passing vehicle must show thesameness with those of the monitored bridge.
This study presents numerical simulation of VBI system and compares the vehicle andbridge vibration. The main purpose of this study is to show the differences between them.
Parametric analysis is carried out in order to discover a condition in which they are identical.
NUMERICAL SIMULATION
A rigid body and spring model is adopted as the vehicle, while the bridge is modeled by finite
1

2

Assisstant Professor
Bechelor student

GFig. 1 VBI system
Table 1The standard parameters of vehicle

Mass𝑚𝑠Stiffness 𝑘𝑠
Damping 𝑐𝑠
Inertia
𝐼𝑃
Distance𝑙
Unsprung- Mass𝑚𝑢
Stiffness 𝑘𝑢
Damping 𝑐𝑢
Sprung-18,000[kg]1.0 × 106 [kg/s2]
1.0 × 104 [kg/s]
64958[kg m2]
1.875[m]1,100[kg]
3.5 × 106 [kg/s2]
3.0 × 104 [kg/s]

Table 2The bridge parameters

Span𝐿LengthFlexural𝐸𝐼
Stiffness
Mass per𝜌𝐴
unit length
Reyleigh
𝛼coefficients 𝛽

30.0[m]1.56 × 1010[Nm]3,000[kg/m]
0.238
0.000

beam elements, as shown in Fig. 1. Their parameters are also shown in Table 1 and Table 2.
The equation of motion of VBI system is described as[𝐌B

𝐋(𝑡)𝐌P 𝒚(𝑡̈ )𝐂B]{}+[()𝐌V𝒛 𝑡−𝐂P 𝐔(𝑡)𝐂V]{𝒚(𝑡̇ )𝐊B}+[()
𝒛 𝑡−𝐊 P𝐔(𝑡)

𝒚(𝑡 )
]{}
𝐊 V 𝒛(𝑡)𝐂 𝒓̇ (𝑡) + 𝐊 P𝒓(𝑡)}={ P𝐋( 𝑡 )𝐌 P 𝑔(1)

where 𝐌B, 𝐂B and 𝐊 B are the mass, damping and stiffness matrices of bridge, respectively.
And, 𝐌V , 𝐂V and 𝐊 V are also those of the passing vehicle. 𝐌P is the mass matrix of thevehicle of the gravity term. 𝐂P and 𝐊 P are the bridge damping and stiffness matrices of theinput to the vehicle. 𝒚(𝑡) and 𝒛(𝑡) denote the response vectors of bridge and vehicle,respectively. 𝐋(𝑡) and 𝐔(𝑡) are the equivalent nodal force distribution matrices, which canbe supposed to satisfy 𝐋(𝑡) = 𝐔T (𝑡). Newmark- method is applied to Eq. (1). The first andsecond undamped natural frequencies of the bridge model are 3.96[Hz] and 15.84[Hz]. The
run speed of the vehicle and the road profile are varied. The road profiles are shown in Fig. 2.
RESULTS AND DISCUSSION
The effect of vehicle run speed is examined, first. The bridge and vehicle responses,

Displacement [mm]0.04

ISO-EXTR-GOOD
EXTR-GOOD
ISO-GOOD
GOOD
ISO-EXTR-GOODx2
ISO-EXTR-GOODx3
STANDARD
ISO-EXTR-GOODx10

0.02
0-0.0205101520
Position [m]

2530

30

0050
Frequency [Hz]0-501020Position [m]3013.3Hz

16.0Hz

10000
5000
0050
Frequency [Hz]Acceleration [m/sec2]-0.5
0Power [m2/sec4]

Acceleration [m/sec2]

015000100-100-1
01020
Position [m]304.00Hz

10000
16.0Hz

5000
0050
Frequency [Hz]Acceleration [m/sec2]-0.5

Power [m2/sec4]

Acceleration [m/sec2]

015000x 10610.7Hz

420050Frequency [Hz]1020
Position [m]30

4x 1069.18Hz
13.6Hz20050
Frequency [Hz](b-2) Run Speed = 10.0[m/s](b-1) Run Speed = 10.0[m/s]0.5306(a-2) Run Speed = 5.0[m/s](a-1) Run Speed = 5.0[m/s]
0.5

1020
Position [m]Power [m2/sec4]

1020
Position [m]10.5Hz2000

5Power [m2/sec4]-0.2
04.15Hz20
100-100

1020
Position [m]30Power [m2/sec4]

04000

Acceleration [m/sec2]

0.2

Power [m2/sec4]

Acceleration [m/sec2]

Fig. 2 The road roughness

2x 10

614.2Hz

19.33Hz0050
Frequency [Hz](c-2) Run Speed = 15.0[m/s](c-1) Run Speed = 15.0[m/s](2) Vehicle (at the unsprung-mass)(1) Bridge (at the position of 10[m])Fig. 3 The response features of different vehicle run speeds (Road Profile: ISO-GOOD)
when the road profile is categorized into ISO-GOOD, are shown in Fig. 3. The blue lines denotethe acceleration responses and power spectra of the bridge. The red ones do those of the vehicle.
The observation position of the bridge is located on L/3 (= 10[m]), so that the first andsecond mode appear. The predominant frequencies (4.00[Hz] and 16.0[Hz]) in the case of therun speed at 15.0[m/s] are close to the first and second undamped natural frequencies of thebridge (3.96[Hz] and 15.84[Hz]), respectively. Those in the case of 5.0[m/s] and 10.0[m/s],
however, are different from the bridge natural frequencies. Fig. 5 shows the acceleration inputsof the travelling vehicle system due to the road unevenness. According to these figures, theroad profile as the input of VBI system dominantly affects bridge response as the outputs.
On the other hand, the vehicle responses shown in the right side of Fig. 3. have
similarity to the bridge responses only around the dominant frequency of the road profile. Itmeans that the vehicle response usually does not match the characteristic of the bridge vibration.
Examples of the bridge and vehicle responses in different road profiles are also shown21.3Hz528.7Hz20050
Frequency [Hz]4.00Hz

10050
Frequency [Hz]01020
Position [m]Power [m2/sec4]

0.5

30

15000
10000

4.00Hz16.9Hz

5000
0050
Frequency [Hz]50-5-1001020
Position [m]30Power [m2/sec4]

4(a-1) Road Profile: ISO-EXTR-GOODx2Acceleration [m/sec2]

x 10

15x 10510.2Hz107.55Hz

50050
Frequency [Hz](a-2) Road Profile: ISO-EXTR-GOODx2
100-10-2001020
Position [m]30Power [m2/sec4]

30

x 10

Acceleration [m/sec2]

1020
Position [m]2Acceleration [m/sec2]

0-0.5050
Frequency [Hz]45.0[m/s](b) 10.0[m/s](c) 15.0[m/s]Fig. 5 The acceleration inputs due to the road profile

0.5-0.507x 100050
Frequency [Hz](a)

10Power [m2 /sec4 ]Power [m2 /sec4 ]10.7Hz100Acceleration [m/sec2]

6x 10

Power [m2/sec4]

Power [m2 /sec4 ]624x 1068.00Hz20050
Frequency [Hz](b-1) Road Profile: ISO-GOOD(b-2) Road Profile: ISO-GOOD(1) Bridge (at the position of 10 [m])(2) Vehicle (at the -mass)
Fig. 6 The response features of different vehicle run speeds (Run Speed = 15.0[m/s])
in Fig. 6. The bridge vibrates mainly around its natural frequencies, regardless of the roadprofile, while the vehicle reacts depending to the road profile. It is shown that the bridge
frequencies due to the traffic loading tends to be around its natural frequencies, while thevehicle frequencies depend on the road profile and tend to be different from the bridge naturalfrequencies. Thus, it is difficult to apply a simple frequency domain analysis to VRA for bridge
damage detection.
CONCLUSION
This study presents the numerical simulation of VBI system and it is cleared that the bridge
predominant frequencies tend to appear around the natural frequencies. The vehicle frequencies,
however, are affected dominantly and directly by the road profile and could not be around thebridge natural frequencies.
REFERENCE
Yang, Y.-B. et al : Extracting bridge frequency from the dynamic response of a passing vehicle,
J. of Sound and Vibration, Vol.272, pp.471-493, 2004.