Rapid algorithm to find optimal step excitations for modal testing of long-span roof structures

A rapid algorithm is proposed to obtain optimal step excitations for the modal testing of long-span roof structures (LRS). Step excitations of LRS are realized by suddenly removing gravity loads. The optimization of step excitations aims to strengthen the contribution of a target mode to the structural free vibration and to suppress the participation of its adjacent modes at the same time. In this way, the target mode can be well triggered without the disturbances of its adjacent modes. The simplified mathematical relationship between the objective indicator vector and the load distribution is established. By solving a bounded-variable least square problem, the optimal step excitations are rapidly acquired. The numerical study of a Geiger cable dome and both numerical and experimental studies of a spatial truss are carried out. The results show that the rapid algorithm can quickly complete the optimization of step excitations, and help the classic Ibrahim Time Domain method greatly improve the identification accuracy of closely spaced modes of LRS.