Delayed resonator for displacement-excited vibration control: combining with a high-static-low-dynamic-stiffness primary structure

Abstract Delayed resonators (DRs) refer to a class of active vibration absorbers driven by the control forces following past (delayed) system states. By tuning the delay, DRs can enable complete vibration suppression at a given frequency. Different from the existing DRs, which mainly focus on force-excited vibrations, this work considers a displacement-excited case where the primary is mounted on a vibrating frame (base). Particularly, the high-static-low-dynamic-stiffness (HSLDS) feature is injected between the primary and the frame, given its widely known benefits in vibration isolation, finally yielding a combined system with a DR and an HSLDS primary structure. Targeting complete vibration suppression, with additional efforts made to seek performance enhancement in the HSLDS case over the classical constant-stiffness (CS) case, the investigation includes dynamical analysis, control parameter tuning, and stiffness optimization. Meanwhile, special attention is paid to evaluating the nonlinear effect of the HSLDS feature, and the shown negligible effects constitute the basis for using limited-order models without compromising accuracy. Finally, experiments showcase a simple yet effective HSLDS mechanism based on magnetic springs. This work not only extends the application scope of DRs but also exploits the mechanical advantage of the HSLDS feature to achieve complete vibration suppression.