Low-Rate Characterization of a Mechanical Inerter

In this study, improved analytical models, numerical parametric explorations, and experimental characterization are presented for a mechanical inerter to bring out dependencies for dynamic mass amplification under low rates (<5 Hz) of excitation. Two common realizations of the inerter-the ball-screw and the rack-and-pinion versions-are considered. Theoretical models incorporating component inertias and sizing were developed for both versions. The dependence of the specific inertance on key design parameters is explored through simulations. Based on these simulations, a prototype rack-and-pinion inerter delivering a specific inertance above 90 was designed, fabricated, and tested under low-rate displacement and acceleration-controlled excitations. The measured specific inertance was found to display an exponential decline with an increase in excitation frequency for both cases. Deviations from predictions are attributable to the frequency dependence of internal stiffness and damping in the fabricated prototype. Using a phase-matching procedure for a representative lumped model, the internal stiffness and damping in the prototype were estimated. Examination of the phase spectra reveals an influence of the excitation frequency on the internal stiffness, damping, and consequently specific inertance. Further, based on the results of this study, design perspectives for such mechanical inerters, which are seeing increasing use in several low-frequency applications, are also presented. It is envisioned that this approach can be utilized to subsume the specific nonlinear characteristics of individual inerters into a simple yet unsimplistic model that can be used to more efficiently and accurately predict the behavior of multi-element, inerter-based systems that employ them.