Concise analytical solutions to negative‐stiffness inerter‐based DVAs for seismic and wind hazards considering multi‐target responses
Ning Su, Zhaoqing Chen, Cong Zeng, Yi Xia, Jing Bian
Abstract
Abstract Practical engineering structures are subjected to hazardous seismic‐ and wind‐ induced vibrations during their lifetime. They should be designed based on capacity and serviceability targets. Similarly, the design of dynamic vibration absorbers (DVAs) should also meet multiple requirements. However, most current analytical approaches are based on a single‐target response and may lead to cumbersome expressions for complicated scenarios. To address these issues, concise solutions to negative‐stiffness inerter‐based DVAs are proposed in this paper. Firstly, a generic analytical optimization approach for H ‐norm solutions considering different response targets of displacement, velocity, acceleration, and transmissibility, is established. Subsequently, the concise solutions are derived based on Taylor's expansion of these analytical solutions by ignoring higher‐order items of the equivalent mass ratio. Finally, the application scope and effectiveness of the proposed concise solutions are discussed. Consequently, the resulting concise solutions are proved to be located close to the pareto fronts of multi‐target optimization results. They have shown superior performances than conventional solutions in controlling the structural capacity and serviceability indicators of a practical five‐story steel frame case under dynamic wind and seismic hazards. Conclusively, the proposed concise solutions are simple in expression and reveal excellent multi‐target performances, which can provide guidance and insights for the optimal design of DVAs.