Targeted modal response control of structures using inerter systems based on master oscillator principle

Although the first modal response generally dominates in structural vibration control, higher-order mode control or multiple-mode control should also be taken into account when higher-order modes are excited. An effective way to accomplish multiple-mode control is to resort to inertial vibration absorbers, wherein the inerter serves as a two-terminal device with dynamic mass amplification and damping enhancement effects. Although previously published studies focused on inerter-based multiple-mode control, analytical design formulae have not been proposed owing to the peculiar mechanism of the inerter. Inspired by the two-terminal, relative-acceleration-related characteristics of the inerter, this study proposes a closed-form design formulation to identify the parameters of inerter systems to achieve targeted multiple-mode control. In this method, the relative deformation at the installation location is considered as the master degree-of-freedom, and the shape of the targeted control mode is considered as a structural deformation shape. In this way, by transforming the complex original structure into a master oscillator with the inerter, the parameters needed for the targeted-mode control can be easily determined based on the use of closed-form design formulae. The proposed targeted control method is applied to a benchmark 10-story building to illustrate how the parameters of inerter systems are designed by the proposed demand-oriented, targeted control method. The comparative analyses between the proposed and previous methods are conducted to demonstrate its superiority. The reductions of the designed inertances compared with alternative methods exceed 90%. Results show that the designed inerter systems can accurately and efficiently realize the targeted control of specific, multiple modal responses. The proposed method is proved to yield a high-precision, targeted-mode control effect, and requires relatively low computational effort. Therefore, it can be easily implemented in an inerter-based, multiple-mode control system.