Equivalent Linearization Methods for a Control System with Clutching Inerter Damper

Inerter-based dampers have gained great popularity in structural vibration control. In this paper, equivalent linearization methods (ELMs) for a single-degree-of-freedom (SDOF) system with a clutching inerter damper (CID) are studied. The comparison of a SDOF system with a CID and an inertial mass damper (IMD) shows the advantage of the CID. Considering that the system with the CID is nonlinear, which is problematic for its performance evaluation and the integrated design of the structure and control system, three equivalent linearization methods based on different principles are proposed and discussed in this paper. The CID is considered to be equal to a combination of an IMD and a viscous damper. The equivalent inertance and damping can be calculated using the obtained formulas for all methods. In addition, all methods are compared in a numerical study. Results show that the ELM based on period and energy is recommended for small inertance-mass ratios.