The Inerter: A Retrospective

Abstract

This article provides an introduction and overview of the inerter concept and device. Careful attention is given to the distinction between the inerter as an ideal modeling element and devices that approximate the ideal behavior. The background is given to the formal definition of the inerter as a mechanical one-port with terminal forces proportional to the relative acceleration between them. Four major methods of construction are described and modeled. The discussion focuses particularly on the notion of terminals, the distinction between a device and an effect, sign reversals, back driving in geared systems, the conceptual aspects of the modeling step for inerter embodiments, and the problem of reverse engineering to discover a purpose. The article includes an analysis and discussion of the rotational inerter, a brief review of the ideas of passive network synthesis that led to the inerter concept, and an analysis and discussion of several examples of integrated mechanical devices. It concludes with an imaginary dialogue between the author and an interlocutor on the understanding and purpose of the inerter.

Inerter assisted robustness of compliant liquid column damper

“…The property of inertance is referred subsequently bypassing the device details. A target inertance is obtained by designing/proportioning of the inerter components, as detailed by Smith 47,48 …”

“…Symbolic representation of an inerter is shown in Figure 3d by illustrating the associated DOFs. The developed force is expressed as 47,48 where u 1 and u 2 are the displacements of terminal 1 and terminal 2, respectively. A dot over a symbol refers to its time derivative, and symbol b refers to the inertance of a linear inerter.…”

An Inerter-Based Dynamic Vibration Absorber With Concurrently Enhanced Energy Harvesting and Motion Control Performances Under Broadband Stochastic Excitation Via Inertance Amplification

“…This consideration motivates the following definitions for the TMDI natural frequency ωΤ and damping ratio ζT ( ) In this setting, the TMDI benefits significantly by the mass amplification effect of the grounded inerter compared to the conventional TMD Giaralis 2014, 2017). This can be appreciated by noting that TMD vibration suppression efficacy improves monotonically as the secondary mass increases (e.g., De Angelis et al 2012) and, at the same time, that the inertance is readily scalable in actual inerter device implementations (Smith 2020). The latter is commonly achieved by leveraging the rotational inertia of a flywheel driven by mechanisms which transform the relative translational motion of the device ends into rotational motion (e.g., Smith 2005, Pietrosanti et al 2020).…”

“…Theoretically, the ideal inerter is defined as a massless linear mechanical element which resists relative acceleration through a constant of proportionality, dubbed "inertance" and measured in mass units (kg) (Smith 2002). Technologically, inerter embodiments with inertance several orders of magnitude higher than the device physical mass have been prototyped and experimentally verified (Smith 2020). This has been widely achieved by considering mechanisms transforming the translational motion of the device ends into rotational motion of a lightweight fast-spinning disk (flywheel) (Papageorgiou and Smith 2005, Wang et al 2011, among other alternatives (Swift et al 2013, Gonzalez-Buelga et al 2015, Liu et al 2018.…”

Design and Tests of a Controllable Inerter With Fluid-Air Mixture Condition

“…Since the concept of the inerter was proposed [1][2][3], the inerter has been applied into several vibration isolation fields, such as vehicle engineering [4][5][6][7], aerospace engineering [8][9], and civil engineering [10][11][12][13][14]. The majority of the inerter is used as a passive element.…”