Frequency analysis of two subsystems coupled by a spring-inerter-damper device and its application to continuous system for vibration control

Two continuous subsystems interconnected by a spring-inerter-damper device are common engineering configurations for vibration control. To address the problem of designing device parameters for optimal vibration control, comprehensive and systematic mathematical analyses are carried out for the minimum 2-degrees-of-freedom (DOF) system which includes two subsystems interconnected by a spring-inerter-damper device. Then, the equivalence between the 2DOF system and the full-scale continuous system is established, which allows the results of the 2DOF system to be directly transferrable to the original full-scale system. Results show that there is an optimal tuning condition in which two roots coalesce and both damping ratios reach equally high value at the first bifurcation. The device parameters at this point are derived mathematically, and used for optimal vibration control. The subcritical and supercritical conditions are also defined and the associated properties are derived. When applied to a continuous rotating beam-tendon system as a case study, the device parameters derived based on the equivalent 2DOF system are shown to be close to the optimal parameters with errors less than 6 %, and the performance of the resulting full-scale continuous system is almost identical to the optimal performance.