Nonlinear energy sinks (NESs) and tuned mass damper (TMD) have achieved excellent control performance. However, their energy and frequency robustness, as well as a large desired slide mass, impede their wide application in practice. To address this limitation, this paper proposes an asymmetric NES that combines two types of inerter NES, the AsymI-1 NES and AsymI-2 NES, to improve the damping robustness of traditional control devices and reduce the damper mass. In addition, the distinction is achieved by adding an inerter between the sliding damper and the top or bottom story. Further, the mathematical formulation of the asymmetric inerter NES is deduced. The working principle of the proposed asymmetric inerter NES is presented, and motion equations of the asymmetric inerter NES-attached system are derived. The proposed asymmetric inerter NES is optimized using impulsive excitation to analyze its energy and frequency robustness. The control performance and wavelet spectrum analyses of the asymmetric inerter NES are conducted under the action of earthquakes. The analysis results show that combining the two asymmetric inerter NESs can help to absorb seismic energy rapidly, limit structural reaction, and ensure good energetic and frequency robustness. Furthermore, the proposed asymmetric inerter NES can significantly decrease the stroke requirement and damper mass.
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