Analytical design of DVAs for marine structures: H ∞ optimization of velocity and acceleration for damped systems

Offshore platforms and ship structures are typical marine engineering systems, for which low-frequency vibration is an urgent problem to solve. The H∞ optimization theory for DVAs on undamped structures has been well established, yet relevant research on damped structures is limited to single-degree-of-freedom systems. This paper investigates the H∞ optimization of DVAs attached to damped structures. Analytical parametric optimization formulas for velocity and acceleration responses are derived using the perturbation method, followed by sensitivity and error analysis. The method is further extended to multi-mode structures, and its applicability is verified through a three-degree-of-freedom system, a thin plate, and a cabin model. The results demonstrate that the proposed formulas achieve high accuracy and can effectively reduce structural vibration responses, as validated by both experiments and simulations. The proposed formulas provide theoretical guidance for the DVA design of damped structures in marine engineering.