Semi-active inerters can modulate inertance and are effective for vibration control under time-varying excitation frequencies. However, conventional inerters and semi-active inerters are predominantly single-axis devices, whereas real structural vibrations occur simultaneously in multiple directions. This mismatch reduces effectiveness under multi-directional excitation and often requires multiple uncoupled devices. In addition, most semi-active vibration control systems rely on external power sources, limiting applicability in power-loss scenarios such as earthquakes or remote installations. To address these limitations, this paper presents a multi-directional magnetorheological semi-active inerter capable of generating tuneable inertial forces with self-powered semi-active control. The inerter employs a gimbal structure to convert planar translation into orthogonal rotational motion of two variable-inertia flywheels, enabling multi-directional modulation of inertance. Meanwhile, two energy harvesting units are also integrated into the inerter, enabling self-powered semi-active operation. A nonlinear two-degree-of-freedom inertance model is derived using the Euler–Lagrange formulation and combined with a bilinear hysteresis representation of the MRVIF. Harmonic characterisation experiments confirm directional invariance and controllable inertance modulation along both axes, with harvested energy sufficient to switch inertance states. Vibration control demonstrations under multi-directional random excitation show reductions in peak relative displacement and RMS acceleration compared with passive configurations. The results demonstrate a self-powered, multi-directional, semi-active inerter exhibiting configuration- and state-dependent inertial behaviour, contributing to the emerging class of nonlinear and variable inertial elements in structural dynamics.
Tran et al. (Wed,) studied this question.