<p>Structural vibrations induced by dynamic loads can severely compromise the performance, stability, and safety of buildings and infrastructure. The conventional tuned liquid column dampers (TLCDs), while effective, often require increased static mass to achieve the desired performance, leading to practical limitations. This paper introduces an enhanced vibration control device, tuned inerter liquid column damper (TILCD), which integrates an inerter with U-shaped and V-shaped TLCD configurations to amplify effective mass without increasing static mass. The main concept leverages H₂ and H_∞ optimisation techniques to analytically determine the optimal frequency and damping ratios of these novel dampers. Using Lagrange’s equation and frequency response functions, exact closed-form expressions are derived for damper design, and structural responses are evaluated under harmonic and stochastic excitations. Comparative analyses show that TILCDs achieve up to 81.04% improvement in displacement reduction and over 60% improvement in acceleration control compared to traditional TLCDs. The study also investigates whether structural displacement and acceleration responses can be simultaneously controlled using the proposed damper, confirming the dual effectiveness of the TILCD. These results demonstrate the effectiveness and robustness of TILCDs in diverse dynamic environments, providing a cost-efficient and practically implementable solution. The analytical approach eliminates the need for iterative design methods and offers strong potential for future experimental validation.</p>