Evaluation of the self-induced vibrations modes of bridge superstructure during monitoring

In the last 20–30 years, bridge condition monitoring during the operational cycle has become increasingly common on the Russian highway network. The monitoring ensures control of the bridge on an ongoing basis in a continuous mode. The task facing the monitoring systems developers is to expand the range of the parameters that can be used in real-time to monitor the bridge’s condition and the safe conditions for its operation. One way is to use indirect parameters obtained as a direct data processing result. Appropriate algorithms for converting information recorded by the system sensors and obtaining new parameters are needed. The most important design characteristics are dynamic characteristics, which include the frequencies and amplitudes of the self-induced vibration modes, and vibration decrements. This article discusses a technique for estimating the dynamic bridge characteristics, namely, the self-induced vibration modes frequencies and amplitudes using experimental data. A dynamic system mathematical model that performs self-induced vibration is considered in the system form with one input signal and n output signals. Formulas for the model frequency response and its components are given: the amplitude and phase response of the system. To calculate the frequency response, power spectra and cross-power spectra are needed, which are obtained using the Fourier transforms of the signal. The article shows how, to reduce the random error, to estimate the mutual spectrum by dividing the realizations into several adjacent intervals (segments) of length T each. The final spectrum (periodogram) is obtained as the arithmetic mean of the segment spectra. Monitoring systems using accelerometers that measure the structure linear accelerations of the record the output signals. One of the accelerometers is considered an input signal source. According to the proposed mathematical model, the self-induced vibration frequency response of the system characterizes the amplitudes and signs of the structure displacements at the accelerometers’ location at different frequencies. The mathematical apparatus considered by the authors is applied to the data obtained on a real object: a bridge crossing over the Volga river on the highway Nizhny Novgorod-Shakhunya-Kirov in the Nizhny Novgorod region — Borsky Bridge. The monitoring of the bridge state stream crossing the Volga by its purpose is control and research, in terms of the form of information presentation over time — continuous, in terms of the speed and synchronism of polling sensors — dynamic. The monitoring purpose is to monitor the bridge structure operation and its operating conditions, including the technical control of the stress-strain state (SSS) parameters. The bridge characteristics and the current monitoring system are given. The results of numerical calculations of the arch span for vibrations are presented. The authors performed periodogram calculations using the mathematical package MathCad using the signals of two accelerometers. To estimate the frequencies and amplitudes of the span structure vibration modes using monitoring data, periodogram calculations were performed using the SpektrKatKross program that implements the proposed algorithm. The correspondence results of the program to the results of the calculations by the program MathCad are shown. The calculated and experimental vibration modes of the span are close. As a result of using the proposed mathematical model, the reliability of this comparison is ensured both in terms of frequencies and in terms of amplitudes.