One of the benefits it offers is that, in lower frequencies, it performs similarly to the TMDs while in higher frequencies it behaves similarly to viscous dampers [41]. Furthermore, a rotational inertial double-tuned mass damper was introduced to enhance the vibration mitigation of the structures [42]. In order to overcome the detuning of the rack-pinion inerter while it is assembled with the TMD, a V-belt CVT was introduced into the TMD-inerter system [43; 44]. In this device, an ideal frequency can be generated, leading to remarkable vibration reduction. New mechanisms are introduced regarding the influence of noise on the device or the reduction of the level of radiated noise from the device. In controlled directivity of the noise method, a lumped mass is employed to minimize the sound pressure [45; 46]. The operation in a limited frequency band is the main defect of passive devices while the structure may be excited by various external frequencies. As a passive TMD is aligned to the primary structure, the primary structure's oscillation is alleviated only in its principal resonance. However, in other bands of frequency the level of response mitigation is undesirable and is even destructive. In fact, there is a sensitivity to variation of the frequency of the external force relative to that of the primary structure, leading to detuning of the TMD and its performance degradation. In this research, a newfound adaptive tuned mass inertance damper (ATMID) is presented to resolve the above-mentioned problems. A novel redesigned CVT in which the transmission of the torque occurs through a set of planets that can be rotated and tilted between two rings is introduced. The proposed device with a new configuration and the special CVT-inert assembling is able to tune the inertance, allowing the adaption of the TMD's frequency. The proposed device possesses the ability to generate an adjustable inertance and frequency via the core of the CVT smoothly and seamlessly. The distinct feature of the proposed ATMID lies in introducing an adaptive TMD in which a very small amount of damping is included due to the internal damping of the CVT (not viscous oil), a variable inertance is also included in the TMD. This variable inertance can generate a variable frequency and a variable inertial force in the TMD. In fact, the initiative of utilizing CVT with a special operation and concept contributed to enabling the introduced ATMID to adjust the frequency to be equal to that of the excitation. Substantially, the adaptive TMDis capable of adapting and retuning itself according to the properly tuned inertance. It also leads to the removal of device detuning. Consequently, a high reduction in the vibration of the primary structure is attained in a vast frequency range by utilizing the ATMID. In this research, to assess the efficiency of the ATMID as well as clarify its controllable dynamic specifications, a single degree of freedom (SDOF) incorporated with an ATMID is simulated while harmonic ground excitation is induced in the primary structure. This research certified the significant potential of the proposed ATMID for harmonically induced structures while the frequency is varied. The remainder of this article is organized as follows. In Section 2, we present the technical design of the device including the details of configuration, the efficiency of CVT, and the analytical model. The device features, as well as the rationale behind the device, are investigated in Section 3. The damping properties of the device and level of motion reduction are considered in Section 4. Finally, a summary of the main achievements is given.