Optimal design of inerter-based absorbers with amplified inertance: from the improved tuned liquid column damper inerter (ITLCDI) to the improved tuned mass damper inerter (ITMDI) and improved tuned inerter damper (ITID)

This paper presents the optimal design of improved inerter-based absorbers to effectively mitigate vibrations in structural systems. The improvement of the inerter is achieved by integrating it within a rhombus truss, composed of rigid rods interconnected by hinges. This arrangement exploits the geometrical amplification effect to enhance inertial properties, thus leading to superior control performance. Specifically, both ends of the inerter are anchored to opposite points along one diagonal of the rhombus, while along the other diagonal, one end is grounded, and the other is linked to the structural system itself or other mechanical systems. The motion of these systems triggers the activation of the inerter, contributing to vibration dissipation. Previous studies have combined this improved inerter with a spring-dashpot unit proposing the so-called Improved Tuned Inerter Damper (ITID). Extending prior research, this study integrates the improved inerter with common passive control devices, such as the Tuned Liquid Column Damper (TLCD) and Tuned Mass Damper (TMD), resulting in the development of the novel Improved Tuned Liquid Column Damper Inerters (ITLCDI) and Improved Tuned Mass Damper Inerter (ITMDI). The optimal calibration for the ITLCDI through an analytical approach is presented, assuming stochastic processes for modeling seismic actions. Furthermore, it discusses how the ITLCDI configuration can be adapted to yield the ITMDI and ITID configurations, providing closed-form solutions for all three absorbers. Validation of the proposed method is performed through numerical simulations, with a thorough analysis conducted to assess the effectiveness of the ITLCDI relative to the ITMDI and ITID configurations.