Railway bridges are excited to forced vibrations during train crossing and destabilization of the ballast bed may result. Thus, instability of the rail position may occur that lead to critical states for trains and passengers, respectively. During the design process of new railway bridges that are built on high-speed railway lines in European countries a dynamic analyses of train crossing must be performed and a limit value of 3.5 m/s² of the maximum vertical bridge deck acceleration must be fulfilled according to EN 1991-2. A second limit value is the restriction of the bridge end rotations due to train crossing to a value of 6.7 ‰ according to the Austrian guideline “Dynamic calculation of railway bridges due to train crossing”.
The arising size of the bridges forced vibration amplitudes due to train crossing depends on both, train specific and bridge specific parameters. Train specific parameters represent the dynamic excitation forces and they are influenced of train speed, axle load and axle distances. The bridge specific parameters are essentially the natural frequencies and the structural damping coefficients. In cases, where the periodic excitation forces due to train crossing meets one of the natural frequencies of the bridge structure, resonant vibrations occur with unwanted large vibration amplitudes.
Within the dynamic analyses of train crossing the natural frequencies of railway bridges are computed by the ratio of bending stiffness to mass per unit length. Both, the stiffness and the mass are taken from the bridge design documents. In a large part the comparison of calculated natural frequencies with frequencies determined by in-situ modal testing show a good agreement. The structural damping of bridges is defined by the Lehr´sche damping coefficient and it cannot be calculated in practical applications. Within numerical simulations of train crossing the Lehr´sche damping coefficient is always chosen according to regulations that are given in EN 1991-2. In case of steel and concrete bridges with span lengths of more than 20 m a value of 0.5 % and of 1.5 % has be chosen, respectively. It will be shown that the damping values that are determined by in-situ experimental modal testing are in most cases significant higher and that the mentioned damping values are quite conservative.
The research project “KOMET” (funded by the Austrian Federal Railways) carried out by the Austrian research company REVOTEC, the research institute AIT and the Vienna University of Technology aims to show the potential and the benefits of assessing dynamic parameters (natural frequencies and damping coefficients) of railway bridges and their non-linear behavior using forced vibration excitation. Another focus of the project is to improve the comparability of measurements carried out by different contractors by updating a current guideline.
In-situ experimental modal tests by application of the forced vibration excitation method were performed to identify the real values of natural frequencies and damping coefficients of different construction types of railway bridges. In addition, conventional dynamic measurement methods like ambient vibration measurement, time decay after train crossing and impact excitation through impulsive hammer are also applied to the tested railway bridges. At first the gained measuring results by application of different excitation methods are compared and discrepancies are discussed. At second the determined dynamic parameters by application of the forced vibration excitation method are compared with calculated values of natural frequencies and with the damping coefficients given in European codes. Limitations of the applied forced excitation method are discussed and approaches for handling these limitations are presented. Detected discrepancies of theoretical expected and in-situ measured dynamic parameters are also discussed in detail and possible reasons for the discrepancies are mentioned. As a main project result a table of realistic damping coefficients for railway bridges of different construction type is elaborated and recommendations for choosing the damping values within dynamic analyses of train crossing are specified.
The aim of the proposed forced vibration excitation method is beside the reliable determination of natural frequencies especially the reliable and reproducible determination of the structural damping coefficients, also by taking changing environmental conditions (temperature) and nonlinear effects (e.g. size of vibration amplitude) into account. In practice it is often observed, that the application of conventional monitoring methods for modal properties of structures, like ambient vibration monitoring show limits in the evaluation of realistic structural damping values. By use of the proposed forced vibration excitation method significant vertical vibration amplitudes are generated and the values of structural damping result more realistic and reproducible. From 2015 to 2017 more than 40 railway bridges of different types with ballast track were measured in summer and winter conditions by use of the forced vibration excitation method. The span length of the bridges varies from 3 to 40 m and the measured natural frequencies varies from 3 to 80 Hz.
The forced vibrations were generated by use of multiple long stroke shakers, which are electrodynamic force generators, where the output is directly proportional to the instantaneous value of the applied current. They can deliver random or transient as well as sinusoidal waveforms of excitation force. The unit employs permanent magnets and is configured such that the armature coil remains in a uniform magnetic field over the entire stroke range - assuring force linearity. Within the performed bridge measurements, a sine-sweep signal was used to excite the railway bridges and the natural frequencies were identified within the frequency domain. For determination of structural damping a manually sweep was performed within the frequency range of interest and the half power bandwidth method was applied.
The performed work within the research project turn out, that the forced vibration excitation method provides reliable and reproducible results for the natural frequencies and structural damping values of railway bridges. Particularly, the structural damping coefficients that result from the application of the half power bandwidth method to the manually generated frequency response function, results in reliable and reproducible values as base for calibrating numerical simulations of train crossing. It is shown, that the in-situ measured structural damping coefficients of framed concrete railway bridges with ballast track are up to 3 times higher than the values given in European codes.
It is concluded, that compared with conventional methods to measure modal properties of bridges, like measuring ambient vibrations, the proposed application of a forced vibration excitation method by use of multiple long stroke shakers, provide more reliable and reproducible values for natural frequencies and structural damping coefficients, respectively.