Equivalent Static Wind Load for Structures with Inerter-Based Vibration Absorbers

Equivalent Static Wind Loads (ESWL) are desired in structural design to consider peak dynamic wind effects. Conventional ESWLs are for structures without control. For flexible structures with vibration control devices, the investigation of ESWL is required. Inerter-based Vibration Absorbers (IVAs), due to the light weight and high performance, gained much research attention recently. This paper established a generic analytical framework of ESWL for structures with IVAs. The analytical optimal design formulas for IVAs with different configurations and installation locations are provided. Subsequently, the solutions to uncontrolled and controlled wind-induced responses are derived based on the filter approach. Finally, the ESWL for controlled structures are presented with a gust response factor approach. The ESWL estimation for a tall chimney controlled by IVAs is illustrated, and the results revealed a significant ESWL reduction effect of the IVAs, particularly for the cross-wind vortex resonance. In the presented framework, the conventional uncontrolled ESWL can be converted to the controlled one with a control ratio. The closed form solution of the control ratio is provided, which enables a quick estimation of ESWL for controlled structures particularly in the preliminary design stage. The presented approach has the potential to be extended to more complex structures and vibration control devices.