An integrated equivalent tuned‐mass‐inerter vibration absorber and its optimal design

Inerters have been widely used in the vibration suppression of automobile and civil structures, due to its large capability in kinetic energy. When applying inerters at the free end of a structure, additional lumped mass has to be involved for obtaining the driving force, which may not be beneficial to the integrity of the device. In this paper, an integrated equivalent tuned mass damper with inerter (ETMDI), having the mass with respect to both translational motion and rotation in a single device, is proposed. First, the equation of motion for the proposed ETMDI system is derived from the Lagrange's equation. The extended fixed-point theory is next used to obtain the closed-form expression for the optimal parameters. Taking a single degree-of-freedom system and a wind turbine tower, numerical simulations are further performed considering base excitations. Compared to the classical TMD and the inerter-based vibration absorber (IDVA-C4), the efficiency and robustness of the proposed ETMDI have been confirmed, showing its potential in energy absorbing and vibration mitigation applications.