Spectral density approach for dynamic analysis of high-speed railway bridges

University essay from KTH/Bro- och stålbyggnad

Author: Alket Ciku; Vlad Gavriliuc; [2022]

Keywords: ;

Abstract: The focus of this thesis is to introduce the concept of train signature in the spectraldensity approach used in the dynamic analysis of simply-supported railway bridges.Due to the increased transportation demands, longer trains with higher axles loadsand top speeds are being developed. To account for these innovations, a series of newtrain load models will be introduced in the upcoming Eurocode. The motivationbehind the concept was to develop a time-efficient, simple method which can becomequite useful after the inclusion of the new train load models. A simply-supported railway bridge of 20 metres has been chosen as the study case.The values of the flexural stiffness and damping values were chosen conventionally,by considering a population of existing bridges in Sweden. The bridge model itselfwas idealized as a single degree of freedom system, considering only its verticaldisplacement. The work has been performed using Matlab, as the method itself requires to numericallyintegrate results, instead of providing a closed-form solution. Time domainmethod was used as a means of verifying the validity of the method at hand, as ityields the most accurate results. Similarly to the frequency domain method, the spectral density approach suffersfrom the low frequency resolution caused due to the insufficient number of samples.The worst case scenario occurs in short span bridges and high train speeds. To account for this problem, two solutions were investigated. The first solution wasto introduce 10 seconds of free vibration to the signal. However, it was dismissed asthe RMS values obtained could not be applicable in real cases. The second solutionwas to extend the train lengths by adding multiple intermediate coaches. By doingso, a steady-state response was reached, which meant that the acceleration RMSvalues could be used to obtain the peak acceleration values. However, the resultsshowed that this approach worked well only in resonant and sub-resonant speeds,while underestimating the response when moving away from these speeds. Finally, a parametric study was conducted, considering both the spectral densityapproach and time domain method. In the parametric study, the damping value,mass, flexural stiffness and span length of the bridge were considered. The effectsof each parameter on the method considered were evaluated.

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