Experimental validation of moving spring-mass-damper model for human-structure interaction in the presence of vertical vibration

Ehsan Ahmadi, Colin Caprani, Stana Živanović, Amin Heidarpour

Research output: Contribution to journalArticleResearchpeer-review


The interaction between structures and walking humans is an important factor in vibration serviceability assessment of slender, lightweight, and low-damping structures. When on bridges humans form a human-structure system and interact with the structural vibration. The conventional vertical moving force (MF) model neglects human-structure interaction (HSI) effects. In contrast, a moving spring-mass-damper (MSMD) model is shown to have the potential to incorporate HSI effects leading to more accurate vibration response prediction. The MSMD model parameters have been much studied in biomechanics. However, the literature lacks an experimental calibration of the MSMD model parameters on a vibrating surface for vibration serviceability design and assessment purposes. Consequently, an experimental-numerical methodology is developed to calibrate the MSMD model parameters in the worst-case (resonance) scenario by matching measured and simulated vibration responses. To facilitate simple implementation of HSI effects into engineering practice, results of simulation using a calibrated equivalent moving force (EMF) model are also shown. The walking force on rigid surfaces along with vibration responses of two lively full-scale laboratory footbridges are measured for 23 test subjects by performing a total of 295 trials on the two structures. A parametric study is first performed on the MSMD model using the experimental results. The experimental results of the Monash footbridge are then used as the training dataset to extract optimal MSMD model parameters. The results from the Warwick footbridge are used to validate the model. The validation tests results show a considerable improvement in the vibration response prediction using both models. It was found that when walking in resonance with the bridge, the walker can be modelled to have natural frequency equal to the resonant frequency of the bridge, and that the damping ratio is larger for heavier walkers.

Original languageEnglish
Pages (from-to)1274-1285
Number of pages12
Publication statusPublished - Feb 2021


  • Equivalent moving force model
  • Footbridges
  • Human-induced vibration
  • Human-structure interaction
  • Moving spring-mass-damper model
  • Vertical walking force

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