Human-structure dynamic interaction: an analytical solution

Human-structure interaction can play a crucial role in influencing human-induced vibrations in structures. In the case of vibrations in the vertical direction, experimental observations suggest that this interaction tends to be beneficial, effectively contributing additional damping to the system. This paper presents a general analytical framework for investigating the impact of human-structure interaction on the dynamic behavior of structures. Building on recent approaches in the literature [1,2], the structure is modeled as a continuous dynamic system, while pedestrians are represented as fixed single-degree-of-freedom oscillators. Focusing on a single vibration mode, an analytical expression for the frequency response function of the coupled human-structure system is derived. The proposed solution is applicable to any pedestrian distribution on footbridges or floors and allows for the inclusion of variability in pedestrian dynamic properties. From the frequency response function, the equivalent dynamic properties of the coupled system are extracted. A parametric study is conducted to explore the influence of varying structural and pedestrian dynamic characteristics. Additionally, two case studies are presented to illustrate the practical application of the proposed model. [1] D. Colmenares, A. Andersson, R. Karoumi, An analytical solution of the maximum response of the coupled multiple parallel modulated pedestrian-bridge system. Structures 57 (2023), 105160. [2] C. Gallegos Calderon, J. Naranjo Perez, C. Renedo, I. Diaz A frequency-domain approach to model vertical crowd-structure interaction in lightweight footbridges. Journal of Sound and Vibration 557 (2023), 117750.