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

The additional inerter-based viscoelastic mass dampers (AIVMD) and additional viscoelastic mass damper inerters (AVMDI) are introduced in this article. H-2 and H-infinity 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, H-2 optimized AIVMD and AVMDI have 53.23% and 57.73% dynamic response reduction capacities while H(infinity)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 H-2 optimized AIVMD and AVMDI, furthermore, 92.14% and 94.36% dynamic response reduction capacities for H(infinity)optimized AIVMD and AVMDI. These optimal closed-form solutions are mathematically accurate and relevant for practical applications.