Investigation of Dynamic Responses and Vibration Serviceability of Temporary Grandstands by a 3 DOF Interaction Model due to Swaying Motion

Abstract

Excessive vibration of temporary grandstand by the crowd has lateral rhythmic motions, which attracted increasing attention in the recent years. This paper focuses on experiments where a temporary grandstand occupied by 20 participants is oscillated by a shaking table with a series of random waves and the crowd-induced rhythmic swaying motions at lateral direction, respectively. The dynamic forces that were induced by participants who have swayed at 0.5–1.8 Hz are recorded by a tri-axial human biomechanics force plate. A new relationship between the annoyance rate and structural acceleration at logarithmic coordinate is investigated and proposed, and the swaying load model is given. Based on these experimental results, a simplified three-degree-of-freedom lumped dynamic model of the joint human–structure system is reinterpreted. Afterwards, combined with a feasible range of crowd/structural dynamic parameters, a series of interaction models are analyzed, the vibration dose value (VDV) of the structure is obtained and discussed, and the notable parameters for interaction model are predicted. The experimental results show that the lateral serviceability limit is 1.29 m/s1.75 and the upper boundary is 2.32 m/s1.75. The dynamic response of model indicated that the VDV of structure will be decreased with increasing the mass of static crowd and damping ratio of the dynamic crowd. The max response of the model is α ≤ 0.6, f2 = 1.8 Hz or α > 0.6, f2 = 1.5 Hz or f1 = 2.5–3.5 Hz. It may be used as a reference value in vibration safety and serviceability assessment of TDGs, to estimate realistically the vibration response on the occasions when the crowds are swaying.