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