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To investigate vibration control and optimal design of transmission lines with tuned-mass-damper-inerter (TMDI), the motion equation of transmission lines with TMDI is established in the paper, and the closed-form solutions of the response spectrum of transmission line displacement are derived by the frequency domain analysis method. The design parameters of TMDI are optimized by fixed-point theory, and the vibration control performance of TMDI is discussed. The results show that the increase in apparent mass ratio has a positive effect on the vibration control performance of TMDI; the vibration control performance is greatly affected by frequency ratio and limited by damping ratio; the increase in both mass ratio and apparent mass ratio reduces the peak values of the displacement response spectra of transmission line with TMDI; however, blindly increasing the apparent mass and mass ratio (β &gt; 0.2 or μ &gt; 0.4) has a limited effect on improving the vibration control performance of TMDI; compared with conventional TMD, the peak values of the controlled displacement response spectrum of the transmission line with TMDI can be reduced by about 12%, and TMDI has a better vibration suppression effect on the transmission lines.

Tuned-Mass-Damper-Inerter Performance Evaluation and Optimal Design for Transmission Line under Harmonic Excitation