An analytical solution of the maximum response of the coupled multiple parallel modulated pedestrian-bridge system

This paper studies analytically the steady state response of the generalised coupled modulated pedestrian-beam system. Pedestrians are considered as modulated spring-mass-damper systems with and without a partially attached mass to the structural system. The governing non-dimensional parameters that defined the system's behaviour are found in an analytical framework. An application of the expression is developed, and a parametric analysis is presented considering a reference pedestrian. The frequency shift effect and the dynamic amplification factor, DAFHSI, of the coupled pedestrian-beam system are characterised. The main contribution of this paper is to provide a closed-form solution of the generalised coupled modulated pedestrian-beam system. This solution can consider any distribution of pedestrians and any definition of the pedestrian SDOF properties. A simple and representative example is presented to demonstrate the utility of the found expression in the context of footbridge dynamics.