The response of grandstands driven by filtered Gaussian white noise processes

TL;DR

This paper develops a semi-analytical method to estimate grandstand responses under active and passive crowd loads modeled as filtered Gaussian white noise, validated through Monte Carlo simulations and frequency domain comparisons.

Contribution

It introduces a semi-analytical approach combining stochastic modeling and lumped biodynamic models for accurate response estimation of grandstands with crowds.

Findings

Semi-analytical estimates closely match Monte Carlo simulations.

The method effectively captures the effects of active and passive crowd dynamics.

Frequency domain estimates provide a useful comparison benchmark.

Abstract

This paper presents a semi-analytical estimate of the response of a grandstand occupied by an active crowd and by a passive crowd. Filtered Gaussian white noise processes are used to approximate the loading terms representing an active crowd. Lumped biodynamic models with a single degree of freedom are included to reflect passive spectators occupying the structure. The response is described in terms of the first two moments, employing the It\^o formula and the state augmentation method for the stationary time domain solution. The quality of the approximation is compared on the basis of three examples of varying complexity using Monte Carlo simulation based on a synthetic generator available in the literature. For comparative purposes, there is also a brief review of frequency domain estimates.