Design of MDOF structure with damping enhanced inerter systems.

An inerter is a two-terminal inertial element that can produce an amplified inertance and enhanced damping when operating with spring and damping elements. Its superior vibration mitigation effect has been proved by previous studies. Although H∞ optimal design of inerter-controlled single-degree-of-freedom structure can be derived based on fixed-point method, rational and theoretical design methods for inerter-controlled multi-degree-of-freedom (MDOF) structures yet need to be developed. In this study, a practical and semi-analytical method based on the damping enhancement principle is proposed for the design of inerter-controlled MDOF structures under earthquakes. To improve the vibration mitigation efficiency, the parameters of inerter systems are distributed based on structural responses, and the required damping coefficient in the inerter systems is minimized to fully utilize the damping enhancement effect of inerter systems. The response mitigation ratio is taken as the targeted performance index to fulfill the demand-oriented design philosophy presented in this study. The stochastic response of the structure is obtained by conducting complex mode superposition. A detailed design procedure and corresponding computer program is developed. Three benchmark structures are employed to exemplify the effectiveness of the proposed design. The analysis results show that the story drifts and story shear forces of the designed structure are effectively mitigated to the target value. In comparison with an existing method (the fixed-point method), the proposed design strategy efficiently exploits the damping enhancement effect, resulting in reducing the damping coefficient and damping force while satisfying the performance demand, thereby producing a rational and economical design. [ABSTRACT FROM AUTHOR]