Development of a multi-passive tuned mass damper, theory and experiments

Transcription

1 Proceedings of the 9th International Conference on Structural Dnamics, EURODYN 4 Porto, Portugal, 3 June - Jul 4 A. Cunha, E. Caetano, P. Ribeiro, G. Müller (eds.) ISSN: 3-9; ISBN: Development of a multi-passive tuned mass damper, theor and eperiments Andreas Andersson, Raid Karoumi, Alan O Connor Division of Structural Engineering & Bridges, Roal Institute of Technolog (KTH), Brinellvägen 3, Stockholm, Sweden Department of Civil, Struct. & Env. Engineering, Trinit College Dublin (TCD), College Green, Dublin, Ireland adde@kth.se, raidk@kth.se, oconnoaj@tcd.ie ABSTRACT: In this paper, a bi-directional multi-passive tuned mass damper is presented. The application for the damper is on vertical hangers of an eisting steel arch railwa bridge. The hangers have been found susceptible to resonance and the resulting stresses results in a reduced service life due to fatigue. Due to different boundar conditions, the natural frequencies of the hangers are different in the longitudinal and the transverse direction. In addition, the natural frequencies increase during train passage, due to increased tensile force in the hangers. A prototpe of the damper has been developed, consisting of two suspended masses coupled in series. Different lateral suspensions are used to obtain different natural frequencies in the longitudinal and the transverse direction. One mass is tuned to the conditions of the full loaded bridge and the other mass to the unloaded bridge. The performance of the damper is verified using controlled loading under laborator conditions and the results are compared with a finite element model. The damper is shown to perform as epected and the motion of the two masses is near uncoupled. Finall, the performance of the damper is verified b in-situ testing on the case stud bridge. KEY WORDS: Tuned Mass Damper; Railwa Bridge Dnamics; Resonance; Frequenc Response Function. INTRODUCTION There is constant demand on railwa authorities to increase both the allowable ale loads and allowable train speeds on eisting railwa lines. For bridges on non-high speed railwa lines, dnamic effects are often accounted for b increasing the static response with dnamic amplification factors, not accounting for the risk of resonance. For bridges with low mass, low natural frequencies and low damping, resonance ma however occur even for moderate train speeds. In combination with long and heav trains, resulting stresses ma cause a significant reduction in the fatigue service life. Previous studies of a steel arch railwa bridge [] and [] have shown that some of the vertical hangers are susceptible to resonance during train passage, which results in a reduced service life due to fatigue. A sstem of passive pendulum dampers were installed [3], tuned to the natural frequencies of the unloaded bridge. During train passage however, the increased tensile force in the hangers show in a significant increase in natural frequencies. This ma cause a detuning to a passive damper sstem. In addition, the boundar conditions of the hanger to main beam connection, Figure, results in different frequencies in the longitudinal and transverse direction. Simulations of different adaptive and semi-active sstems showed great potential in improving the performance [4], accounting for both the loaded and unloaded bridge conditions. Implementations of such sstems are however a challenge, especiall when based on variable stiffness control. A proposed compromise is instead a sstem of passive dampers with several natural frequencies to account for both the loaded and unloaded conditions as well as the difference in the longitudinal and transverse direction. In this paper, the development of a bi-direction multipassive tuned mass damper (bi-mtmd) is presented. The performance of the damper is verified under controlled loading and compared with numerical models. From free vibration tests of the unloaded bridge hanger, the natural frequencies f = 4.3 H and f = 3.6 H and appertaining damping ratios ζ =. % and ζ =.3 % was estimated. During train passages, the natural frequencies increased to f F = 6.3 H and f F =. H. The modal mass of the hanger is calculated to 3 kg. Figure. Details of a bridge hanger. NUMERICAL MODEL OF THE DAMPER The initial design of the damper is based on the model illustrated in Figure. It works as a combination of a tuned mass damper and a pendulum damper. The mass consists of two steel rings that are suspended in wires and coupled in series. The length L is chosen sufficientl long to avoid

2 Proceedings of the 9th International Conference on Structural Dnamics, EURODYN 4 significant coupling between the upper and lower ring. Each ring is also connected to the hanger b horiontal springs and dashpots. The upper ring is tuned to the natural frequencies of the loaded hanger and the lower ring to the natural frequencies of the unloaded hanger. During eperimental testing, the prototpe damper is connected to a sliding base and ecited using a load shaker. The mass m b of the sliding base is lumped to a single point and the properties of the load shaker estimated b a stiffness k b and damping c b. The rings and the wires are modelled with Euler-Bernoulli beam elements. From an eigenvalue analsis, the modes in Figure 3 are obtained. The modes show that the upper and lower rings are near uncoupled. hanger upper mass a L shaker rigid links lower mass wire a d b L L hanger upper ring ) base plate mass ) c b k b m b lower ring Figure. FE-model of the bi-mtmd. base a b F base Figure 4. Prototpe damper during load shaker tests. steel ring wire support foam a) b) c) d) Figure 3. Modes of vibration. 3 EXPERIMENTAL TESTING The prototpe of the bi-mtmd is depicted in Figure 4. Each steel ring has a mass of.3 kg. The wires consists of mm nlon strings and has a length L = mm. The mass of the base m b =.3 kg and from a separate test of onl the base and the load shaker, a natural frequenc of 9 H and damping of 3% is estimated. The horiontal connection between the ring and the hanger consists of coil springs and blocks of foam material, illustrated in Figure. The damper is primar tuned b modifing the coil springs. The foam is primar used to prevent ecessive vibrations and to add additional damping, but also contributes to the stiffness. hose clamp coil spring Figure. Illustration of the components of the bi-mtmd. 3. Setup and instrumentation The damper is calibrated under controlled laborator conditions using the setup illustrated in Figure 4. The sstem is instrumented with uni-aial accelerometers a, a and a b. The base displacement d b is measured with an LVDT and the input force F is measured with a load cell. The sensor specifications are provided in Table. Table. Sensor specifications. sensor: make: range: a,a Entran EGCS-A ±g a b Sensotec 6-F48- ±g F Visha, Model 6 ± kg d b Sangamo DC LVDT ± mm The laborator equipment consists of the following: LDS V4 Electro-dnamic shaker. LDS PAL Linear Power Amplifier. Tektroni TDS Oscilloscope. TGA4 waveform generator. Visha 7-3-SM data acquisition sstem (4 bit).

3 Proceedings of the 9th International Conference on Structural Dnamics, EURODYN 4 The effective data resolution for the sstem is about 8 bit, corresponding to about -3 m/s for the accelerometers,.4-3 mm for the LVDT and. N for the load cell. The performance of the sensors is studied in a separate test, b mounting all sensors onto the sliding base and removing the damper. The difference in peak acceleration between a and a is about 4%. Integrating the acceleration two times give similar results as measured with the LVDT and differentiating the measured displacement two times give similar results as the acceleration. Also, dividing the measured force with the known mass of the base results in similar acceleration. 3. Frequenc Response Function The dnamic characteristics of the damper can be studied b the frequenc response function (FRF) of the measured response. An input load with linearl variable frequenc and constant amplitude is sent to the load shaker via the oscilloscope and the linear power amplifier. A min sweep is performed with a 3V input gain and a frequenc range from to H and then back to H. All results are normalied with respect to a unit base displacement. The corresponding transfer function is calculated as the time domain response of the single sided Fourier transform of the measured base displacement. The displacement of the damper is estimated based on time integration of the corresponding acceleration. The FRF is obtained directl from the peaks of the resulting time response. A comparison between the FRF obtained from the eperimental data and the FE-model is presented in Figure 6. The natural frequencies ) to 4) corresponds to the modes a) d) in Figure 3. The resulting dnamic characteristics estimated from the eperiment are summaried in Table. The damping is estimated using the Half-Power Bandwidth method. R d ) ) 3) f (H) 4) eperiment FE-model Figure 6. FRF, comparison between eperiment and FEmodel. Table. Estimated natural frequencies and damping ratio of the complete prototpe damper, based on a min sine sweep load. (H) (%) (mm) (N) f 4.3 ζ. d 9. F.4 f 3.9 ζ 6. d 7.4 F 4. f 6.6 ζ 6. d 8.4 F 3.3 f.6 ζ 7. d. F 7. To stud the influence of the foam material, a separate test of the damper is performed with the foam removed. The results are presented in Table 3. Table 3. Estimated natural frequencies and damping ratio of the prototpe damper without foam material, based on a min sine sweep load. (H) (%) (mm) (N) f 3. ζ. d 6. F 3.9 f 3.4 ζ.4 d. F 7. f 4.9 ζ. d 3. F 49.8 f 4.9 ζ.6 d 4.8 F 3.7 The FE-model is calibrated based on the eperimental data, with the natural frequenc and stead-state displacement as the primar objective functions. All calibrated input parameters are given in Table 4, both with and without the foam material. The foam results in a stiffness increase of about a factor of in the -direction and about 4% in the - direction. As illustrated in Figure, the foam is onl present in the -direction and the increase in the -direction is mainl due to shear. The increase in viscous damping is about a factor for both directions of the lower ring, a factor 3 and 4 for the upper ring in the - and -direction correspondingl. The large ratio of increase is due to the inherent low damping of the setup with onl coil springs. Table 4. Input parameters for the FE-model of the damper, calibrated based on eperimental data. Complete damper Damper with no foam (kn/m) (Ns/m) (kn/m) (Ns/m) k.7 c 3.6 k.38 c.6 k.6 c 4. k.4 c.8 k.7 c. k.8 c. k.4 c 6.43 k.79 c Response to harmonic load blocks To simulate the conditions on the bridge, the damper is subjected to a harmonic load block. The base displacement is about. mm and the frequenc change from 6.3 H to 4. H, Figure 7. This corresponds to the loaded and unloaded hanger conditions. The frequenc in Figure 7b is estimated b a Short Time Fourier Transform with a second window and 9% overlap. The response of the damper is presented in Figure 8. The displacement is estimated b time integration of the measured acceleration. As a verification, the integrated base acceleration shows good agreement with the measured base displacement presented in Figure 7a. The measured base displacement is also used as input to the FE-model. During loading, the upper ring is first activated, Figure 8a. The amplitude of the lower ring is about mm, slightl higher than the base displacement of. mm. During the change in frequenc, the displacement of the upper ring is rapidl attenuated and the lower ring activated. The FE-model is shown to reproduce a similar response. 3

4 Proceedings of the 9th International Conference on Structural Dnamics, EURODYN 4 d (mm) f (H) b) 3 Figure 7. Input for harmonic load block, a) base plate displacement, b) forced frequenc. d (mm) d (mm) - - eperiment FE-model - - b) Figure 8. Damper displacement due to the forced vibrations, a) upper ring, b) lower ring. 4 NUMERICAL MODEL OF THE BRIDGE A 3D FE-model of the bridge has been developed, illustrated in Figure 9. The properties of the bridge are described in detail in [] and []. It is a simpl supported tied arch steel railwa bridge, carring a single unballasted track. The span length is 4 m. The bridge deck consists of main girders, secondar stringer beams and cross beams. The whole bridge is modelled with 3D Euler-Bernoulli beam elements. To simulate the detail depicted in Figure, the lower end of the hanger is assumed pinned in the transverse direction and clamped in the longitudinal direction. The upper end of the hanger is assumed pinned in both directions. The natural frequencies of FE-model shows good agreement with previous field measurements reported in []. The FE-model of the damper, Figure, is assembled into hanger in the global FE-model of the bridge, Figure 9. The length of hanger is 6.9 m, the upper ring of the damper is located at. m from the lower end of the hanger. This is not the most optimal location, but is the same as used during later full-scale testing. a) a) arch bi-mtmd hanger rigid link main beam Figure 9. 3D FE-model of the bridge. Passing trains are simulated b moving point loads directl onto the stringer beams. The dnamic simulations are performed using direct time integration and geometrical nonlinearit, to account for the increase in aial force of the hangers during train passage. A tpical freight train is studied, consisting of 9 wagons and an ale load of kn. Simulations are performed at different speeds, to investigate resonance in different hangers. The resulting displacement of hanger when running at 9 km/h is shown in Figure. For the current speed, resonance is obtained for longitudinal bending. The damper is shown effective it mitigating both the forced vibrations during the train passage and the following free vibrations. d (mm) d (mm) Figure. Displacement of hanger during train passage, from the FE-model. The frequenc content from the displacement of hanger is shown in Figure. In the -direction, the unloaded frequenc is 4.3 H and the loaded frequenc 7 H. The damper is able to mitigate both these frequencies. In the -direction, the unloaded frequenc is 3. H and the loaded frequenc.3 H. The damper is mainl able to mitigate the unloaded frequenc and ma be slightl detuned for the loaded frequenc. 4

5 Proceedings of the 9th International Conference on Structural Dnamics, EURODYN 4.6 d.4... d f (H) Figure. FFT of the displacement from hanger. FULL-SCALE TESTING The performance of the damper was further studied during insitu tests on the case stud bridge. Measurements of passing trains were recorded both with and without the damper mounted on the hanger. The installed damper is shown in Figure. d (mm) d (mm) Figure 3. Displacement of hanger during train passage, estimated from measured acceleration..3.. d.3.. d f (H) Figure 4. FFT of the displacement from hanger. Figure. Photo of the installed damper on hanger. The displacements of hanger during train passages were estimated based on measured accelerations. The time response is shown in Figure 3. The displacements in the -direction is of similar magnitude as the FE-model, but larger in the - direction. One reason ma be different train speeds or ale distances in the FE-model and the real train. A clear tendenc of vibration mitigation is found for all ecept the forced vibration in the -direction. Studing the corresponding frequenc content in Figure 4, it is found that the damper is slightl detuned at that frequenc. 6 CONCLUSIONS From the development of the bi-mtmd, the following conclusions are drawn. - The developed damper was found to be relativel uncoupled, although the two masses were connected in series. - A combination of coil springs and foam material was used to achieve the target tuning frequencies and sufficient damping. The foam contributed to both stiffness and damping. - Good agreement was obtained when comparing the eperimental results with the numerical model under various loadings. - Simulations using a 3D FE-model of the bridge showed significant vibration mitigation when implementing the damper. - In-situ measurements verified that the damper is able to mitigate vibrations during both forced and free vibrations in two directions simultaneousl. It ma however be rather sensitive to detuning.

6 Proceedings of the 9th International Conference on Structural Dnamics, EURODYN 4 ACKNOWLEDGMENTS The development of the presented multi-passive tuned mass damper was performed within the Long Life Bridges project, a Marie Curie Industr-Academia Partnerships and Pathwas project funded b the European Commission 7 th Framework Programme (IAPP-GA--8676). The funding is kindl acknowledged. The eperimental work was carried out at Trinit College Dublin, Department of Civil, Structural and Environmental Engineering. A special thank goes to Dr. Kevin Ran and the laborator staff at the Department for the help in manufacturing and testing the prototpe damper. The full-scale tests on the case stud bridge were funded b the Swedish Transport Administration. The instrumentation was performed b KTH. REFERENCES [] A. Andersson and R. Malm, Measurement Evaluation and FEM Simulation of Bridge Dnamics, MSc-thesis, the Roal Institute of Technolog (KTH), 4. [] R. Malm and A. Andersson, Field testing and simulation of dnamic properties of a tied arch railwa bridge, Engineering Structures, 8(), pp. 43-, 6. [3] M. Hortmanns, Ljungan Bridge, Ånge Sweden, Design of dampers for the hangers 3 to 6, Report W983/, Prof. Sedlacek & Partner. [4] A. Andersson, R. Karoumi, A. O Connor, Vibration mitigation of railwa bridges using adaptive damping control, IABSE Rotterdam, 3. 6