Lateral Parametric Vibration of Footbridge under Pedestrian Excitation considering the Time-Delay Effect

Pedestrian excitation may consequently cause large-scale lateral vibration of the long-span softness of footbridges. Considering the influence of structural geometric nonlinearity, a nonlinear lateral parametric vibration model is established based on the relationship between force and speed. Taking the London Millennium Footbridge as an example, the Galerkin method is applied to formulate parametric vibration equations. In addition, the multi-scale method is used to analyze the parametric vibration of footbridge system theoretically and numerically. The paper aims to find out the reasons for the large-scale vibration of the Millennium Footbridge by calculating the critical number of pedestrians, amplitude-frequency, and phase-frequency characteristics of the Millennium Footbridge during parametric vibration. On the other hand, the paper also studies the influence parameters of the vibration amplitude as well as simulates the dynamic response of the bridge during the whole process of pedestrians on the footbridge. Finally, the paper investigates influences of the time-delay effect on the system parameter vibration. Research shows that: the model established in the paper is reliable; the closer the walking frequency is to two times of the natural frequency, the fewer number of pedestrians are required to excite large vibrations; when the number of pedestrians exceeds the critical number in consideration of nonlinear vibration, the vibration amplitude tends to be stable constant-amplitude vibration, and the amplitude of vibration response is unstable constant-amplitude vibration when only linear vibration is considered; the following factors have an impact on the response amplitude, including the number of pedestrians on footbridge per unit time, damping, initial conditions, and the number of pedestrians in synchronized adjustment. At last, when considering the lag of the pedestrian’s force on the footbridge, the time-lag effect has no effect on the amplitude but has an effect on the time needed to reach a stable amplitude.

Damage accumulation comparison for various vibration test profile generation methods applied to a complex payload

There are potential sources of uncertainty when using default or generic profiles for vibration testing, particularly for large and complex payloads ( Warren and Joiner, 2019 ). Replacing these severities with custom profiles generated using measured data offers one alternative; however, care must be taken not to select an inappropriate or inaccurate method. This research details the methodology and results of a trial which involved the design and implementation of a series of vibration tests, each to simulate a mixed-terrain environment applied to a complex payload. A systematic approach was used to develop and execute a test plan via the design of experiments method. An estimate of the damage potential for each was formed using Miner’s rule (linear damage accumulation) applied to direct strain gauge data. This approach was compared with damage measured during a time waveform replication style test to be used as a baseline. The results of this test can be used to guide test specifiers and programme-level acceptance test guidelines and may be useful in implementing or guiding standards in this space. In addition, the damage measured in a series of increasing amplitude vibration tests (with an identical power spectral density) was compared with predicted values to assess the gain linearity assumptions often used in accelerated vibration testing. The research is unique as the authors could not source a thorough trial comparing the damage produced using a range of different profile development methods with a complex, real-world payload. Test houses and test specifiers seeking to improve the accuracy of their tests should consider the key findings and guidance in this article.

Evaluation of Measurement Accuracy of the MEMS Accelerometer for Long Period and Large Amplitude Vibration

Health monitoring systems are used to assess building damage immediately after an earthquake and have become widely utilized in Japan. For example, the system developed by the authors has been installed in more than 60 buildings since 2014. Such systems mostly rely on accelerometers to estimate the building performance. Recently, Micro electro mechanical system (MEMS) accelerometers have been increasingly applied for such uses due to their economic advantages. However, MEMS accelerometers are known to have relatively low measurement accuracy for certain frequency band excitations compared to servo type accelerometers. Past research has been undertaken to test their measurement accuracy, however, few studies review their performance under long period and large amplitude seismic motions. Evaluation of measurement accuracy in such conditions is essential since the system is also installed in tall buildings and isolated buildings with relatively long natural periods. Therefore, this study evaluates the measurement accuracy of the MEMS accelerometer under long period and large amplitude vibration based on the results of shake table testing.

The fastest insight into the large amplitude vibration of a string

This paper recommends a simple and excusive approach to a strongly nonlinear oscillator. Its frequency property can be immediately obtained by the simplest calculation. The results show that the method leads to an approximate solution with relatively high accuracy. Considering the simplest solution process, this paper provides a highly efficient tool for fast determination of the amplitude-frequency relationship of a nonlinear oscillator. The large amplitude vibration of a string is used as an example to illustrate the solution process.