Numerical Simulation of Crowd-Induced Vibrations Using Duhamel's Integral

Inga A.J.V.; Huertas J.E.D.; Pérez P.R.; Terbullino G.F.M. · SSRG International Journal of Civil Engineering (2026) · DOI: 10.14445/23488352/ijce-v13i6p114

Resumen

Crowd-induced vibrations in footbridges represent a relevant issue in the design of lightweight structures. The numerical simulation performed in this research, which is based on Duhamel’s integral, allows for the estimation of the dynamic response to pedestrian loads. Within this simulation, the structure is initially modeled as a Single-Degree-of-Freedom (SDOF) system that is subjected to ramp, harmonic, and pedestrian-type excitations, which allows for validating the numerical implementation against already known analytical solutions. After this, a simplified modal model of a supported beam is adopted, considering only the first vibration mode. The footfall force is represented through harmonic functions adjusted by walking speed and the Dynamic Load Factor (DLF), including the random distribution of speeds in individual walks and in crowds. The simulations, developed in Python, show that the system responds with increasing amplitudes when the step frequency approaches the natural frequency. In the case of crowds of 200 pedestrians, maximum displacements close to 2.50 mm and amplification of the modal envelope were observed during the minutes of greatest overlap. The model is efficient and applicable in preliminary design stages. Its limitations include structural linearity and the absence of pedestrian–structure interaction, although it provides results consistent with the reviewed literature.

Instituciones: Universidad Continental; Universidad Nacional de Barranca