The optimum inerter-based additional viscoelastic mass dampers for dynamic response mitigation of structures

Abstract

The additional inerter-based viscoelastic mass dampers (AIVMD) and additional viscoelastic mass damper inerters (AVMDI) are introduced in this article. H₂ and $H_{\infty }$ optimization schemes are utilized to derive the optimal closed-form solutions for these novel dampers analytically. A parametric study performs to investigate the sensitivity of the optimal design parameters with other system parameters such as damper mass ratio, inerter mass ratio, and stiffness ratio. Thus, a higher damper mass ratio, a higher inerter mass ratio, and a higher stiffness ratio are recommended to design optimum novel dampers for achieving robust vibration reduction capacities. Therefore, H₂ optimized AIVMD and AVMDI have $53.23\%$ and $57.73\%$ dynamic response reduction capacities while $H_{\infty }$ optimized AIVMD and AVMDI can provide $72.97\%$ and $75.57\%$ dynamic response reduction capacities subjected to harmonic excitation, respectively. In addition, random-white noise excitations are also applied instead of harmonic excitation to cross-check the accuracy of the optimal design parameters. The overall result shows that $74.24\%$ and $82.17\%$ dynamic response reduction capacities for H₂ optimized AIVMD and AVMDI, furthermore, $92.14\%$ and 94.36% dynamic response reduction capacities for $H_{\infty }$ optimized AIVMD and AVMDI. These optimal closed-form solutions are mathematically accurate and relevant for practical applications.

Keywords:

• Additional inerter-based viscoelastic mass dampers (AIVMD)
• additional viscoelastic mass damper inerters (AVMDI)
• standard linear solid models (SLS)
• H₂ and H${}_{\infty }$ optimization
• dynamic response reduction capacities

Acknowledgement

The authors would like to acknowledge the Inspire faculty grant, grant number DST/INSPIRE/04/2018/000052 for partial financial support for the project. SC would like to acknowledge the MHRD grant received from IIT Delhi during the period of this research work.

Disclosure statement

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this article.

Data availability statement

All data, models, and code generated or used during the study appear in the submitted article.