Dynamics Analysis of a Variable Stiffness Tuned Mass Damper Enhanced by an Inerter

A tuned mass damper with variable stiffness can achieve vibration reduction without changing the resonant frequency, but the large mass limits its engineering applications. To overcome this drawback, a novel tuned mass damper is proposed with the stiffness adjusted by a PI controller and the mass block replaced by an inerter. The tuned mass damper is attached to a two-degrees-of-freedom primary structure, and the dynamic equations are established. The frequency responses are obtained from a harmonic balance method and verified by numerical simulations. With the mass block of the tuned mass damper replaced by an inerter, the additional weight is reduced by 99%, and the vibration reduction performances are improved, especially in large excitation conditions. The vibration reduction rate increases with larger negative stiffness ratio and larger inertance ratio, while unstable responses appear with the parameters exceeding the thresholds. The optimum negative stiffness ratio and inertance ratio are searched by a frequency change indicator, and the maximum vibration reduction rate can reach 87.09%. The impulse response analysis shows that the proposed tuned mass damper improves the energy absorption rate. The primary structure and the vibration absorber engage in 1:1, 1:2, and 1:3 internal resonance with different impulse amplitudes. This paper aims to promote and broaden the engineering applications of the variable stiffness system and the inerter.