Probability-based prediction of multi-mode vibration response to walking excitation

Abstract

In vibration serviceability checks of footbridges, a force induced by a single person walking is usually modelled as a harmonic force having a frequency that matches one of the footbridge natural frequencies. This approach assumes that, among the infinite number of harmonics a walking force is composed of, only a single harmonic is important for a vibration serviceability check. Another usual assumption is that the footbridge can be modelled as an SDOF system, implying that only vibration in a single mode is of interest. In addition, due to the deterministic nature of this approach, it cannot take into account inter- and intra-subject variabilities in the walking force that are now well documented in the literature. To account for these variabilities, a novel probabilistic approach to carry out a vibration serviceability check is developed in this paper. Factors such as the probability distribution of walking frequencies, step lengths and amplitude of walking force for its five lowest harmonics and subharmonics are taken into account. Using walking force time histories measured on a treadmill, the frequency content of the force was investigated, resulting in the formulation of a multi-harmonic force model. This model can be used to estimate the multi-mode response in footbridges. This was verified successfully on an as-built catenary footbridge structure. Although only the vibration response of footbridges was analysed in this paper, the force model proposed has the potential to be implemented in the estimation of floor vibration as well, where multi-mode response occurs more frequently. The model is easily programmable and as such could present a powerful tool for estimating efficiently the probability of various levels of vibration response due to single person walking. Therefore, the proposed probability-based methodology has the potential to revolutionise the philosophy of the current codes of practice dealing with vibration serviceability of structures under human-induced vibration