Many kinds of oscillators, springs, and damping system compose vibration reduction system in civil structures. Since the invention of the tuned mass damper (TMD) device a century ago, it has become a very important technology in structural control. TMDs can effectively suppress the response of civil structures under harmonic or wind excitations. To improve the damping capacity of TMDs in reducing the vibration of structures under seismic loads, a large mass ratio should be used, but TMDs are still ineffective in suppressing the seismic peak response of high-rise buildings. The inerter-based dynamic vibration absorbers (IDVA), including tuned inerter dampers (TID) and tuned mass-damper-inerter (TMDI), have been investigated in recent years. The advantage of using a TID and TMDI comes from the adoption of gearing in the inerter, which equivalently amplifies the mass. The mass ratio of an inerter is very high; hence, its mechanical properties and reliability are vital. A novel damper device, accelerated oscillator damper (AOD), has been proposed recently. Gear transmission systems are used to generate an amplified kinetic energy of the oscillator to reduce the oscillations of the structures. The AOD system is superior to the traditional TMD system in short time loading intervals or under the maximum seismic loads.