The optimum enhanced viscoelastic tuned mass dampers: Exact closed-form expressions

Abstract

This paper introduces the inertial amplifier viscoelastic tuned mass dampers (IAVTMD). The viscoelastic materials are implanted inside the core material of the inertial amplifier tuned mass dampers. The standard linear solid models are applied mathematically to formulate the viscoelastic material. H₂ and H _∞ optimization mechanisms apply to derive the exact mathematical closed-form formulations for optimal design parameters for novel inertial amplifier viscoelastic tuned mass dampers. The optimum IAVTMD installs at the top of the structures to mitigate the dynamic responses, determining the dynamic responses analytically through transfer function formation. At first, IAVTMD’s dynamic response reduction capacity compares with the conventional tuned mass damper’s (CTMD) dynamic response reduction capacity. As a result, H₂ optimized IAVTMD’s dynamic response reduction capacity is significantly 20.87% and 26.47% superior to two well-established H₂ optimized conventional tuned mass damper’s dynamic response reduction capacity. In addition, H _∞ optimized IAVTMD has 15.48% more dynamic response reduction capacity than H _∞ conventional tuned mass damper. H₂ and H _∞ optimized tuned mass damper inerters with optimal closed-form solutions are introduced in this paper. A higher damper mass ratio and a lower inerter mass ratio are recommended to produce H₂ and H _∞ optimized tuned mass damper inerter (TMDI) with a lower frequency and damping ratio in an affordable range. Accordingly, H₂ and H _∞ optimized IAVTMD’s dynamic response reduction capacities are significantly 6.94% and 23.29% superior to H₂ and H _∞ optimized TMDI’s dynamic response reduction capacity. The closed-form expressions for optimal design parameters of inertial amplifier viscoelastic tuned mass dampers and tuned mass damper inerters are mathematically correct and effective for practical applications.