Analytical optimization of the tuned viscous mass damper under impulsive excitations

•A Pole-inspired optimization methodology for TVMDs dealing with impulse loads.•Analytical design formula for TVMD structure with the highest convergence speed.•Optimized TVMD-structure with a timely response to impulses and a low peak response.•Maximum response spectra for the preliminary design of inerter within the TVMD. The inerter-based damper has proven as an efficient vibration suppression device for steady responses in a broad frequency band. However, the inerter-based structures may experience an impulsive loading process, in which the dynamic performance and pertinent design method remain unknown. Dealing with this, this study proposes a time-decay rate-based optimal design methodology for a typical inerter-based damper, tuned viscous mass damper (TVMD), to suppress the impulse-induced vibration, successively deriving the analytical formula to facilitate the demand-oriented design. Considering the impulsive circumstance, the mechanical model of the TVMD-based structure is established, and a pole-based analysis is performed to quantify the functionality of TVMDs for the transient response attenuation. Inspired by the pole-based analysis result, a time-decay rate-based optimal design method and corresponding analytical formula are proposed to maximize the attenuation rate of TVMDs. Through the implementation of TVMD-based structures, the effectiveness of the pole-based design method is demonstrated by the dimensionless analysis, and then its advantages are illustrated through a comparison with the previous design method. Furthermore, a series of maximum response spectra are established to quantify the dynamic performances of TVMDs. The results show that the pole-inspired design method guarantees the TVMD improved transient attenuation rate and degrees, in comparison with the widely used fixed-point method. In addition, the provided transient response spectra can be adopted as a guideline or reference for the performance evaluation of the TVMD-equipped structure and the preliminary design of TVMDs to meet the expected vibration suppression demand for impulsive excitations. [Display omitted]