Influence of inerters on the vibration control effect of series double tuned mass dampers: Two layouts and analytical study

In this paper, two configurations of series double tuned mass damper with inerters (SDTMDI) are investigated: grounded type (G-SDTMDI) and inserted type (I-SDTMDI). For the former layout, two inerters relate each tuned mass to the ground, while they are inserted between any two adjacent masses in the latter layout. Implementing on a harmonically forced primary system of single degree of freedom, their optimal design is conducted by using an extended version of fixed points theory. The present study suggests that for a given total tuned mass, the vibration control effect of G-SDTMDI is solely controlled by the total inertance, because of which one of the two grounded inerters can be removed, and the vibration control performance will not be influenced under the condition that the amount of inertance remains unchanged. Meanwhile, the control effect delivered by I-SDTMDI is dictated by the inerter relating the primary system and its adjacent tuned mass. Finally, it is analytically and numerically proven that grounded inerters can render the vibration control effect more pronounced, featured by a decreased peak amplitude and an enlarged frequency bandwidth of vibration reduction. The only potential detrimental effect observed is by incorporating an inerter between the host structure and its adjacent tuned mass. In this case, the vibration amplitude of host structure is amplified, and the effective plateau of vibration reduction is narrowed.