外文翻譯--基于振動試驗數(shù)據(jù)下彈性支座的狀況評估（英文）

1、Condition assessment of elastic bearing supports using vibration dataMoatasem M. Fayyadh ?, H. Abdul RazakDepartment of Civil Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysiaa r t i c l e i n f oArticle hi

2、story:Received 22 June 2011Received in revised form 21 November 2011Accepted 7 December 2011Available online 11 January 2012Keywords:Support conditionsElastic rubber bearingNatural frequencyMode shapeReinforced concrete

3、girdersa b s t r a c tThe performance of structures such as bridges, machine foundations and base isolated buildings are verymuch affected by the condition of their elastic bearing supports, which eventually deteriorate

4、due towear and tear or which can be damaged during the service life of the structure. In this study, the dynamicparameters, namely natural frequencies and mode shapes are used to detect the deterioration of the elas-tic

5、bearing supports of a simply supported bridge girder. For this purpose, force vibration testing was con-ducted on a reinforced concrete bridge girder supported at the ends by rubber bearings to simulate theactual conditi

6、ons in a bridge deck. Three different levels of deteriorations were investigated namely thatof no deterioration, partial deterioration, and full deterioration, whereby rubber with different stiffnesswas used to simulate

7、the different deterioration levels. Vibration data were obtained for two cases i.e.an undamaged girder and a damaged girder after being subjected to a load exceeding its service limitfor flexure. A direct relationship wa

8、s observed between the dynamic parameters and the elastic bearingstiffness. Based on the results obtained in this study, the natural frequency of mode 3 is a good indicatorof the deterioration in elastic bearing support

9、conditions while mode 1 is the most sensitive to changes insupport conditions. The Modal Assurance Criteria (MAC) index can be a useful indicator to identify differ-ent causes of deterioration in the structural system. I

10、n order to confirm and verify the observations, fur-ther tests were conducted on a different beam with more deterioration levels in the elastic bearingstiffness. The results support the deductions made regarding MAC and

11、bending frequencies.? 2011 Elsevier Ltd. All rights reserved.1. IntroductionHealth monitoring of engineering structures has gained a lot of interest over the last few years. Many engineering structures suffer damage and

12、deterioration when exposed to various loading and environmental changes during their lifetime. This seriously affects structural performance and may even lead to catastrophic struc- tural failures. Thus, inspection and t

13、esting of structural compo- nents for deterioration and damage is essential when deciding on the maintenance and repair strategies for at-risk structures. A cur- rent alternative approach to conventional structural testi

14、ng meth- ods is dynamic testing, which acquires modal parameters and relates these to the health status of a structure. The fundamental idea underlying the dynamic approach is that modal parameters, namely natural freque

15、ncy, mode shape, and modal damping, are functions of physical properties of the structure, such as mass, damping, stiffness and the support conditions. Therefore, any change in the physical properties or support conditio

16、ns causes detectable changes in the modal parameters. Elastic bearing pads are widely used for supporting bridge girders, and as base isolationof tall buildings to reduce seismic demand. The bearings are ex- posed to var

17、ious loading conditions and environmental changes which cause deterioration of its stiffness with time. Monitoring of changes in elastic bearing stiffness is very important in ensuring timely maintenance or replacement t

18、o prevent occurrence of any serious damage to the structure. Several studies on the use of the modal parameters as an indi- cator for damage identification have been conducted. Some of these studies were concerned with i

19、ssues related to use of these modal parameters in determining the magnitude and localisation of damage based on the relationship between dynamic and physi- cal properties, and concluded that modal parameters are good ind

20、i- cators for damage detection [1–7]. Abdul Razak and Choi [8] investigated the effect of steel corrosion on the natural frequencies of RC beams. The authors concluded that the first natural fre- quency for the RC beam w

21、ith a lower corrosion level decreased by 1%, while for the RC beam with a higher corrosion level the de- crease was 4% and deduced that the bond at the steel–concrete interface played a significant effect. Ismail [9] inv

22、estigated the ef- fect of crack damage in RC beam on its natural frequencies. Flex- ural crack damage was induced by applying load at the mid-span of the beam for three loading cycles. A comparison was made based on the

23、datum frequencies before applying the load to the beams. It was found that the frequencies were reduced for all the0950-0618/$ - see front matter ? 2011 Elsevier Ltd. All rights reserved.doi:10.1016/j.conbuildmat.2011.12

24、.043? Corresponding author.E-mail addresses: moatasem.m.f@gmail.com (M.M. Fayyadh), hashim@um.edu.my (H. Abdul Razak).Construction and Building Materials 30 (2012) 616–628Contents lists available at SciVerse ScienceDirec

25、tConstruction and Building Materialsjournal homepage: www.elsevier.com/locate/conbuildmatBy substituting Eq. (5) into Eq. (7) , the following relation is found;2 1fn? ?@fn ¼ 1EI? ?@ðEIÞ ð8Þwhich

26、implies that a change in flexural rigidity (EI) contributed to doubling the change in natural frequency. This directly relates thechange in the stiffness to the change in the frequency with an assumption of validity for

27、linear and nonlinear structural systems.The frequency based stiffness index can be defined as:Frequency based stiffness index ¼ 2: 1 ? fi;d i; c? ?? 100% ð9Þwhere fi,c and fi,d are the natural frequency at

28、 ith mode for control and damaged beam, respectively.3. Experimental setupIn order to investigate and verify the proposed approach to evaluate the level of deterioration of the elastic bearing support stiffness and to id

29、entify the cause of the deterioration, a scaled down RC girder was used to simulate a bridge girder supported on elastic bearings. The RC girder was simply supported at both ends and designed according to ACI-318-08. The

30、 span length of the girder was 2200 mm, with cross sectional area of 150 mm width by 250 mm depth. The concrete of the girder has a compres- sive strength of 35 MPa, tensile stress 3.86 MPa, and modulus of elasticity 28,

31、000 MPa. The concrete girder was reinforced with two 12 mm diameter bars as flexural reinforcement with a yield stress of 515 MPa, and 8 mm diameter bars with 320 MPa yield stress spaced at 100 mm intervals as shear rein

32、forcement, as shown in Fig. 1. For the purpose of evaluating the level of the elastic bearing deterioration, an undamaged RC girder was utilised with the sup- ports having three different bearing stiffnesses in order to

33、simulate the levels of deterioration. For the cases of no deterioration (Level 1, L1) and partial deterioration (Level 2, L2), rubber pads with stiff- ness of 10 MN/mm and 3 MN/mm, respectively were used. In addi- tion,

34、for the case of full deterioration (Level 3, L3), the girder was supported directly on the underlying structural elements to simu- late elastic bearing with zero stiffness. Table 1 shows the elastic bearing support condi

35、tions adopted in this study, whereby six cases were considered. The cases considered validate the effect of the deterioration level on the modal parameters of the girder whenthere is deterioration of a specific level or

36、different deterioration level at both the supports. The test girder was supported either on rubber pad i.e. no deterioration or partial deterioration cases, or on the underlying structural element i.e. on steel rollers w

37、ith rubber pad removed for the full deterioration case as shown in Fig. 2. For the purpose of investigating the ability to identify the cause of the deterioration, the RC girder was damaged by applying a point load at qu

38、arter-span to induce flexural and shear stresses. The load was applied gradually at a rate of 4 kN/min up to 55 kN, which was higher than the service limit load of 45 kN. After the damage was induced the load was release

39、d, and the vibration data acquired for the three different bearing stiffnesses. In this manner, the effect of both load induced damage and elastic bearing deteri- oration can be captured from the results. In order to obt

40、ain the natural frequency and mode shape, modal testing was performed using the transfer function technique on the RC girder. The girder was randomly excited by a white noise signal. The excitation signal was produced by

41、 a signal analyser, then amplified by a power amplifier, and finally passed onto the shaker that produced the vibration, which was permanently positioned at the soffit of the girder and coincident with reference point nu

42、mber 38 as shown in Fig. 3. The input force was measured by means of a force transducer mounted onto the soffit of the girder and con- nected to the shaker by means of a flexible drive rod. The response signal was picked

43、 up using a single general purpose low impedance accelerometer having a sensitivity of 100 mV/g. A total of 12 accel- erometers were used and the accelerometers were roved from point to point until all the measurement po

44、ints were covered. The measurement points were located on the top surface of the gir- der as shown in Fig. 3, with points 1, 24, 25, 48, 49 and 72 located at the supports. The distance between each measurement point was

45、95 mm and 60 mm in the longitudinal and transverse direc- tions of the girder, respectively. Finally, both input/output signals were fed into a signal analyser for computing the transfer func- tions. The curve fitting pr

46、ocess was performed on the transfer func- tion spectrums obtained to extract the modal parameters i.e. natural frequency and mode shape. The modal test was conducted on the girder for the datum case when there was no det

47、erioration. This procedure was then repeated on the girder under different elastic bearing support conditions. The modal test setup and the girder test conditions are shown in Fig. 4.4. Results and discussionThe first si

48、x bending modes obtained from the experimental work on the undamaged and damaged girder, were utilised in investigating the effect of the elastic stiffness of the support on modal parameters, when the deterioration was i

49、dentical at both supports and when there was a difference in deterioration between left and right end supports. The elastic bearing support conditions considered are no deterioration, partial deterioration and full dete-

50、 rioration and the results and discussion highlights the effects on the Frequency Response Function patterns, on the mode shapes using the Modal Assurance Criteria (MAC) as given in Eq. (1) and on the natural frequencies

51、 by means of frequency based stiffness index as given in Eq. (9).4.1. Frequency Response FunctionDuring the modal testing, the Frequency Response Function (FRF) was acquired. Mathematically, the FRF is defined as the Fou

52、- rier transform of the output (acceleration) divided by the Fourier transform of the input (force). In general, the parameter estimation routines are curve fits in the Laplace domain. The next stage ofmodal testing invo

53、lved the analysis of the measured FRF data to find the theoretical model that most closely resembled the behaviour of Fig. 1. Details and dimensions of tested RC girder.618 M.M. Fayyadh, H. Abdul Razak / Construction and