## 5 Conclusions  
In this research, a newfound vibration reduction device named the ATMID is introduced in which a ball-screw inerter is engaged with a novel redesigned CVT. In the presented CVT with the new configuration and special CVT-inerter assembly, torque transmission happens due to the use of a set of tilting and rotating planets positioned between two rings. The presented ATMID can generate changeable inertance through the seamless controlling of the transmission ratio of the motion of the screw to the gyration of the flywheel. The function of inertance alteration enables the device to produce a smooth variability in its frequency. Therefore, the tuning of the frequency of the ATMID relative to that of the external force can be provided and the device retuning can be eased. By equating the frequency of the ATMID to the frequency of the external excitation, substantial damping properties and vibration mitigation are achieved in an extremely large band of frequency.  
The performance of the introduced ATMID in a harmonically induced SDOF structure was also assessed and compared with PTMD-controlled and uncontrolled cases. At the frequency of, for example, 7.13 (rad/s), where the efficiency of the PTMD with a mass ratio of 0.2 is degraded, the ATMID with a mass ratio of 0.1 and various inertances behaves much better. Noticeable oscillation suppression is obtained for the ATMID with a 56%  
Figure 12: ATMID inertial force-displacement correlation curve at frequencies of 10 and 7.13 (rad/s).  
Figure 13: Total resistant force-displacement curve of PTMD and ATMID at frequency of 7.13 (rad/s).  
response improvement compared to the PTMD-controlled structure and with 21% when compared to uncontrolled. Results showed that the lesser the damping and higher the mass ratio of ATMID, the higher the damping properties would be. The proposed ATMID with a transmission ratio of 0.45-2.2 offers considerable vibration reduction in an enlarged frequency range in the circumstances that the structure is derived with variable frequency.  
Moreover, the concept and capability of the proposed ATMID to achieve the alterable inertance utilizing CVT are demonstrated. The experimental test of the ATMID under seismic and harmonic forces, as well as the investigation of various control algorithms, will be our next research topics. In addition, parametric uncertainty modeling [48], as well as the effect of internal/external noise would be the subjects in our future research. However, expanding the CVT ratio to enhance the device performance would be an attractive challenge.  
Conceptualization, M.A.S. and J.Y.; methodology, M.A.S. and J.Y.; software, M.A.S.; investigation, M.A.S., J.Y., F.W. and X.W.; writing--review and editing, M.A.S., J.Y., F.W. and X.W. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the \"National Natural Science Foundation of China, Grant No. 52078293, 51908352\" and the \"Science Research Plan of Shanghai Municipal Science and Technology Committee, Grant No. 18 DZI205603, 20 dz1201301\".  
Not applicable.  
Some or all data, models, or code that support the findings of this study are available from the authors upon reasonable request.  
We thank Shanghai Jiao Tong University and the Department of Civil Engineering for the use of laboratory equipment and facilities.  
The authors declare no conflict of interest.