MONITORING OF DYNAMIC PARAMETERS OF STEEL BRIDGES BY VIBRATION TESTS 1 INTRODUCTION

Transcription

1 MONITORING OF DYNAMIC PARAMETERS OF STEEL BRIDGES BY VIBRATION TESTS J. Bien Wroclaw University of Technology, Poland P. Rawa Wroclaw University of Technology, Poland J. Zwolski Wroclaw University of Technology, Poland Abstract Forced vibration test is a method enabling us to analyse the changes of dynamic characteristics of steel bridge structures. In some cases it helps monitor their technical condition. In this paper a procedure of a monitoring system applied by team from the Wroclaw University of Technology is described. A comprehensive computer-based system for programming and control of vibration tests as well as for data acquisition and processing is presented. As an example of practical use of the monitoring system, results of steel footbridge tests are shown. The tested suspended structure after renovation was equipped with mass dampers thus special attention was paid to the identification of dynamic characteristics changes caused by the dampers. 1 INTRODUCTION Modern constructions of steel bridges are more and more daring, interesting and slender. For this reason, and of course for the sake of a structure safety and users comfort, all dynamic parameters of such a type of construction should be carefully monitored. One of the monitoring technologies is dynamic parameters testing carried out by means of vibration tests. This technology can be used for a systematic control of bridge condition changes and the results can be used for the assessment of the structure. Many practical applications [1, 2] showed that the methods of structural changes detection and evaluation based on tracing the changes of modal properties of the structure can be effective in early detecting of changes in the structure condition. The methods are especially efficient when the access to the bridge is difficult and when damages are invisible but have an influence on modal parameters of the structure. The vibration test method is also applicable to many other fields of structure analysis, for example: FEM models adjustment, analysis of sensitivity to structural changes, serviceability analysis, spectral analysis, nonlinearity analysis, etc. The application presented in this paper shows the efficiency of the testing method in solving serviceability issues related to the vibration of a footbridge deck. During the last years the Wroclaw University of Technology (WUT) team has developed a method of testing and evaluating of bridge structures condition based on vibration tests. Several preliminary tests of bridges and footbridges have been carried out to calibrate the method and to assess its practical usefulness as well as sensitivity to weather conditions. It has been shown already [3, 4, 5] that temperature and humidity fluctuations have an indirect influence on modal properties of a structure causing changes in structural material properties. Various aspects of the application of vibration tests in monitoring of steel bridges are analysed by WUT team in the Integrated Research Project Sustainable Bridges Assessment for Future Traffic Demands and Longer Lives [6], within 6 th Framework Programme of EU. 1

2 2 MONITORING PROCEDURE The developed system is intended for a systematic identification of dynamic characteristics of structures for fast and relatively cheap monitoring of a bridge technical condition. It is used for the evaluation of bridge condition on the basis of changes in modal parameters which are estimated periodically. The first session of the bridge tests (Figure 1) should be conducted on the new structure before its opening to traffic or at the beginning of the monitoring process (for bridges in operation). The procedure begins with creating a theoretical model of the structure. It can be a FEM model that serves for predicting eigenvalues and modeshapes of the structure by means of the modal analysis. This information is used for the preparation of the tests in terms of sensors and the exciter locations on the structure as well as for choosing measured physical quantities. Next, an experimental modal analysis divided into four separate steps is conducted. The first step of the analysis is the Resonance Curve Method (RCM). Its main goal is the estimation of vibration amplitudes at frequencies from the range assumed at the test preparation stage. As a result of the test, the resonance frequencies are obtained. Secondly, the Half Power Bandwidth Method (HPBM) is performed in order to obtain damping coefficients based on the identified resonance curves. Thirdly, the damping coefficients are estimated by the Logarithmic Decrement Method (LDM). The results of HPBM and LDM are confronted to obtain more reliable damping estimations. The Mode Shape Identification is performed as the last step. Mode shapes of the structure are identified at the resonance frequencies found in the RCM. The results of the presented procedure are used for a comparison with the values obtained in the theoretical modal analysis which enables us to adjust and to refine the theoretical model. All collected data is stored in the bridge database together with all the photographs, drawings and notes related to the bridge. The next test sessions of the monitoring process (Figure 2) should be conducted systematically during the bridge operation and also after each renovation or rebuilding. Parameters of each monitoring test are taken from the database in order to perform the identification of the structure modal parameters in the same way and in the same conditions as the initial test. On the elementary level of the evaluation of the current results in comparison with the previous ones, a decision is taken whether the structure should be analysed in a more detailed way or not. The decision is made with the observed differences between the results of the consecutive tests and the precision achieved in the test. If the discrepancies between the tests results are more distinct than the precision of the test, the reasons can be investigated on the advanced level of the analysis. A more detailed analysis consists of the identification of possible structural changes or/and damages influencing the modal parameters of the structure. When neither structural changes nor damages are identified, differences between ambient conditions during the tests or bias error in data processing can be a possible source of differences between modal parameters of the structure and a repetition of the test should be considered. In the case of detecting of a structural damage an effort can be made to find its location as well as its intensity and extent. Some practical hints concerning the damage identification are given in [13]. In the case of significant changes of construction modal parameters, a system operator can make a decision on additional detailed or special inspection. Simultaneously, after each consecutive testing session, the theoretical models of the structure should be updated according to the current tests results. The analysis of the parameters of the model updating procedure (change of material elasticity modulus, local reduction of elements stiffness, etc.) can also be helpful in future structure condition assessment. 2

3 Figure 1 Procedure of bridge initial testing by means of the vibration exciter Figure 2 Procedure of bridge condition monitoring based on the vibration tests 3

4 The main goals of the bridge monitoring system are: determination of a set of modal parameters of the structure in its virgin state, before the start of operation or at the beginning of the monitoring process, detection of the bridge structural changes (boundary conditions, change of the structure stiffness/mass) or structural damages by means of the analysis of changes in modal parameters during operation of the structure, estimation of location and, if possible, the intensity and extent of the detected damages, creation of a database of modal parameters of bridge structures as a basis for monitoring of the condition changes. The application of exciters to examine dynamic behaviour of bridge structures has many advantages in comparison with other methods of excitation used in the dynamic tests. The most important of them are as follows: full control of exciting force amplitude and frequency, the possibility of exciting force location in various places on the tested structure, the possibility of resonance frequencies identification in a wide range of frequency (a mass of the exciter is negligible in comparison with a mass of the tested structure), the possibility of keeping constant parameters of excitation (i.e. an exciting force, a location, an excitation frequency) for a long time, the repeatability of the excitation parameters even after a long time, relatively low costs of vibration tests, small disturbances in traffic. The analysis of the research and practical application results [7, 8, 9] discloses also several problems related to the forced vibration tests: the necessity of improvements in exciter construction and control techniques, the mode shape identification carried out in field tests is sometimes sensitive to ambient conditions, especially to changes of temperature and humidity [3, 4, 5], structural changes and damage detection and location based on forced vibration tests require high precision measuring equipment and advanced methods of data processing, more tests and analyses are needed for the determination of the correlation between location and intensity of possible damage and mode shapes affected by it. Many research teams have developed various approaches [4, 5, 8, 9, 10, 11, 12, 13] to solve this issue. 3 VIBRATION TESTS IN MONITORING OF THE FOOTBRIDGE 3.1 The tested structure The described procedure of monitoring was applied to the steel structure of a footbridge in Wroclaw (Figures 3a and 4). The structure has a steel deck m long which is suspended on two towers m high. The deck is constructed with two steel pipes of 457 mm in diameter and with a grid of steel elements. The pavement on the bridge was built with wooden elements. Detailed information can be found in [14] and [15]. Static and dynamic proof load tests carried out after reconstruction works revealed that dynamic parameters of the footbridge cannot be accepted. The first and the second natural frequency were close to common pace rate for slowly walking pedestrians (from 1 to 2 Hz) and resonances occurrence is highly anticipated. Additional risk derives from very possible synchronisation of many people passing over the footbridge because it is located between a recreation area and a busy street. Due to these issues, the structure was equipped with three mass dampers (Figures 3c and 3d) and after their installation the structure was monitored and efficiency of the dampers was assessed by means of vibration tests. 4

5 a) b) c) Figure 3 d) The tested footbridge: a) general view before the installation of the dampers, b) the exciter used for tests, c) the damper in the middle of the span, d) the damper in ¼ of the span 3.2 Initial test of the footbridge A theoretical analysis of the footbridge structure carried out before the initial tests showed that the two lowest eigenfrequencies are equal 1.14 Hz and 1.51 Hz and the corresponding mode shapes are the first antisymmetric and the first symmetric mode. The information was used for programming the tests. As a source of excitation the inertial exciter designed and constructed at WUT was used (Figure 3b). The exciter generates a series of impulses of defined frequency which is done by falling and rising a mass about 40 kg. The exciter was put in ¼ of the span, the accelerometers were fixed in ¼ and ½ of the span and two LVDT gauges for displacement measurement were placed near the support No. 1 (Figure 4). A sampling frequency of the measuring device (Spider8 from HBM, Germany) was set on 200 Hz and the time of data acquisition was about 4 minutes which gives Hz resolution of FFT results in frequency domain. The test was programmed and controlled by means of a portable computer with software MANABRIS that serves also for data acquisition and preliminary processing. Following the procedure shown in Figure 1, the RCM was applied to create resonance curves and investigate resonance frequencies. The stepped sine test was carried out with the range from 1.29 Hz to 1.95 Hz with 0.01 Hz frequency step in regions close to theoretically estimated eigenfrequencies. In each frequency step the acquired acceleration time history was filtered in a narrow band according to the excited frequency and the envelope of vibration amplitude for each sensor was estimated. The results are presented in Figure 5. In the investigated range, the two expected resonance frequencies are visible: Hz and Hz. The attenuation of vibration amplitudes at these frequencies is also visible for the sensor 1/2-us-horizontal-session I (horizontal vibrations), however, the amplitude level is very low. 5

6 Figure 4 Test setup The next step included a calculation of damping coefficients with the Half Power Bandwidth method (HPB) using the data from the resonance curves. For this purpose the common formula was used [13]: f r f f δ = (1) where δ is the damping coefficient, f 1 and f 2 are half power bandwidth frequencies and f r is the resonance frequency. The fraction of critical damping for the first mode was equal 0.46% and for the second mode 0.71%. The identification of the damping coefficients by means of the HPB method can be biased due to a leakage present in sparse sampled data, thus the obtained values of damping were confirmed by the Logarithmic Decrement Method (LDM). In order to obtain naturally damped vibration of one mode, the exciter was set on a fixed frequency equal to the resonance frequency identified in the RCM test. After the vibrations became of constant amplitude, the exciter was turned off and the vibrations started decreasing. It is known that a level of damping depends on a vibration amplitude especially in such nonlinear structures as a suspended footbridge. The recorded free vibrations were used for damping estimation. Firstly, the measured deflections were filtered using a passband Chebyshev II of 3 rd order filter to obtain an approximation of 1 DOF system vibrations. Secondly, the maximal deflections were found and the amplitudes were numbered. Using the formula: 1 A δ = k 2n ln (2) π Ak +n where n is a natural number, A is amplitude of vibration and k is a number of vibration amplitude. Different values of δ were obtained applying various values of n and k. Initially, the formula (2) was used with k = 1 and n = 1 for consecutive amplitudes producing an instantaneous value of a damping coefficient. Then the formula (2) was applied to increasing n and for k = 1, k = 20, k = 30, k = 40, k = 60, k = 80 and k =

7 The results of damping identification using the LDM are shown in Figure 6. Finally, the obtained mean values of damping coefficients are 0.43% for the first mode and 1.09% for the second mode. The values are coarsely close to the obtained using the HPB method which shows conformity of both identification methods. The second conclusion is that the obtained values of damping are very low which has been underlined in the conclusion after the first load tests of the renovated footbridge [14]. The last stage of the initial tests was the Mode Shape Identification (MSI). The test was carried out using the reference accelerometer 1/4-ds fixed (see Figure 4) and two other accelerometers roved from one cross-section to another. During the identification of mode shapes, the exciter was set in ¼ of the span as it is shown in Figure 4. The response of the structure at the stable harmonic excitation was acquired in 51 points: 34 points in vertical direction and 17 in transverse direction. The mode of vibration obtained in this way is in fact an operational deflection shape at the known excitation conditions. The excitation frequency was close to resonance and for the sake of that it can be considered as a mode shape. The results of the MSI for the first mode are shown in Figure 7. At each measuring point a standard deviation of the estimated value is marked as a measure of the amplitude fluctuation. 3.3 Monitoring test of the footbridge Following the recommendations given by WUT team after accomplishing proof load tests, the owner of the bridge decided to equip the structure with tuned mass dampers to cut down the amplitude of vibration induced by normally walking people. After detailed analyses 3 dampers were installed under the footbridge deck: one (2310 kg of active mass) to damp the second mode which has the maximum response in the middle of the span and two other devices (935 kg of active mass each) in ¼ and in ¾ of the span to damp the first antisymmetric mode. The second session of the test was carried out after the mass dampers installation. The aim of the investigation was to confirm efficiency of the installed devices and to check their influence on modal parameters of the structure. Special attention was paid to damping estimation and to the investigation of the natural frequencies shift due to an increase in the structure mass. 1.0E+00 Acceleration amplitude [m/s 2 ] 1.0E E E E E-05 1/4-ds-session I 1/2-ds-session I 1/2-us-session I 1/2-us-horizontal-session I 1/4-ds-session II 1/4-us-session II 1/2-ds-session II 1/2-us-session II Hz Frequency [Hz] Hz Figure 5 Resonance curves before (session I) and after (session II) installation of the dampers (1/4 one quarter of the span, 1/2 half of the span, ds downstream, us upstream) 7

8 a) Vertical displacement [mm] start k=20 k=30 k=40 k=60 displacement point-to-point start-to-point 20-to-point 30-to-point 40-to-point 60-to-point 80-to-point 100-to-point k=80 k= % 0.66% 0.55% 0.44% 0.33% 0.22% 0.11% % of critical damping % Time [s] b) % 4.5 displacement start point to point 4.0 start to point 20% Vertical displacement [mm] Time [s] k=4 4-to-point end 15% 10% 5% 0% % of critical damping Figure 6 Results of the LDM for vibrations of the 1 st mode: a) before the installation of the dampers, b) after the installation of the dampers During session II the scanned frequency range was from 1.00 Hz to 2.00 Hz with step 0.02 Hz and in regions close to the resonance frequencies, identified in session I, the step was set to Hz. The device used to excite vibration of the structure was the same in both sessions. The resonance curves obtained during both sessions are shown in Figure 5. The response of the system in the investigated range of frequency after the installation of the dampers is drastically lower than before. It should be noted that in the regions close to resonance identified in session I, some signs of nonlinearity were observed during session II. The amplitudes of vibration observed at these frequencies were more unstable in time. Damping of the structure identified by the LDM in session II was around 10% (see Figure 6) for the first mode so it can be concluded that the efficiency of the dampers is quite good. It generally confirms the behaviour of the structure presented in Figure 5 where the results of the second session show a mild hill rather than a steep peak within the range of Hz. The MSI during session II was carried out taking a denser grid of measuring points and the results are presented in Figure 7. There is a visible difference in the shapes between the lines obtained during both sessions mainly due to different distribution of the structure mass with and without the heavy dampers. 8

9 Normalized deflection shape [-] downstream line - session I upstream line - session I downstream line - session II upstream line - session II Distance from the support No. 1 [m] Figure 7 Normalized operational deflection shapes for the first mode identified during both test sessions (excitation frequency Hz) Unnormalized values of vibration amplitudes in case of session II were about 10 times lower than the observed ones during session I. The same proportion is visible between the appropriate resonance curves presented in Figure 5 at the resonance frequency (1.343 Hz). 4 CONCLUSIONS The testing procedures included in the presented monitoring system have been tested and calibrated during two sessions of tests carried out for a steel suspended footbridge in different structural conditions. On the one hand, the comparison of the two sessions showed a drastically different behaviour of the structure after the installation of three mass dampers. The amplitudes of forced vibration within the frequency range between 1.00 and 2.00 Hz, were 10 times lower at the same excitation level. Damping of the structure for the two modes in that frequency range changed from 0.43% and 1.09% up to 10%. On the other hand, the monitoring system consisting of particular procedures and tests applied to the footbridge structure proved its efficiency and confirmed its usefulness also in applications to light and flexible bridge structures like steel footbridges. Taking into account the experience from vibration tests of various bridge structures, it can be concluded that the presented technology is an efficient tool for monitoring a bridge condition, with special preferences to steel structures. The conducted analyses and the obtained results show the usefulness of the developed complete portable system with computer-based control and data acquisition for monitoring of road and railway bridges as well as for footbridges. The methodology needs further calibration and standardization to become a popular method of bridge testing and monitoring. 5 REFERENCES [1] De Roeck G., Peeters B., Maeck J., Dynamic Monitoring of Civil Engineering Structures, Computational Methods for Shell and Spatial Structures, IASS-IACM, 2000, M. Papadrakakis, A. Samartin and E. Onate (Eds.) ISASR-NTUA, Athens, Greece,

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