This paper proposes a combined dynamic vibration absorber and establishes a coupled dynamic model of an elastic simply-supported beam equipped with a dynamic vibration absorber. Using the modal superposition method, analytical expressions for the amplitude-frequency response of different vibration modes are derived. Focusing on the first-order mode of the elastic beam, analytical solutions for the optimal tuning ratio, optimal stiffness ratio, and optimal damping ratio are obtained based on the H∞ optimization criterion and fixed-point theory, along with the corresponding optimal operating range of the inerter . The validity of the derived design formulas is further verified through the finite difference method. The results indicate that connecting the inerter between the primary and secondary systems does not enhance the vibration reduction performance. In addition, the proposed dynamic vibration absorber demonstrates exhibits excellent vibration suppression capability for the first-order mode of the elastic beam and effectively broadens the vibration absorption frequency band.