Generic optimal design approach for inerter-based tuned mass systems

Abstract

Inerter-based tuned mass systems (ITMSs) have been successfully applied to control the vibration of structures. The control performance of ITMSs is significantly affected by their design parameters. The practical aspects such as installation location and variant type also influence the effectiveness of ITMS. How to obtain optimal parameters considering these aspects is a challenging task. To date, most investigations on the optimal design of ITMSs have been conducted independently and the resulting design formulas were expressed in different manners, which brings difficulties to the practical application. A systematic design method that is applicable to various ITMSs and considers installation locations is currently needed. In order to address these aspects, in this paper, a generic optimal design approach is proposed which provides a basic framework for systematically evaluating and comparing the control performance of various ITMSs. In the proposed method, a generic representation model (GRM) is proposed to parametrically describe various ITMSs including installation locations. Next, based on GRM, the corresponding analytical H∞ and semi-analytical H2 optimal solutions are derived considering different conditions (white noise, wind and seismic excitations). By combining the H∞ result (basic format) and H2 result (numerical data), an equivalent mass ratio approach is proposed and the corresponding empirical formulas are formed. Based on the equivalent mass ratio, two practical criteria are proposed to evaluate the inerter enhancement effect and select the suitable variant type. Finally, through a slender chimney case, the applicability and effectiveness of the proposed design approach, empirical formulas and criteria are validated.