Robert G. Parker

We report an easy-to-make, resonance-based mechanism to realize negative rotational inertia. The device consists of three parts: a heavy inner core, a lightweight outer shell, and rubber connections between the core and shell. We theoretically predict and experimentally observe the negative rotational inertia in the range of 100–230 Hz. The experimental values are obtained via measurements of vibrational response. We further clarify the relation between the bandwidth of negative inertia and the bandgap in a chain consisting of an array of negative-inertia units. The findings reveal a unique property different from conventional systems in classical physics and offer an opportunity for metamaterial designs.

We study the dissipative bistable Duffing oscillator with equal energy wells and observe fractal patterns in the parameter space of driving frequency, forcing amplitude, and damping ratio. Our numerical investigation reveals the Hausdorff fractal dimension of the boundaries that separate the oscillator's intrawell and interwell behaviors. Furthermore, we categorize the interwell behaviors as three steady-state types: switching, reverting, and vacillating. While fractal patterns in the phase space are well known and heavily studied, our results point to another research direction about fractal patterns in the parameter space. Another implication of this study is that the vibration of a continuous bistable system modeled using a single-mode approximation also manifests fractal patterns in the parameter space. In addition, our findings can guide the design of next-generation bistable and multistable mechanical metamaterials.