Synthesis of mechanical networks: the inerter

TLDR

The paper addresses the synthesis of passive mechanical one‑port networks, noting that the mass element is uniquely grounded while other elements are not. The authors introduce the inerter, a device that serves as the true network dual of the spring. The device is defined as a two‑terminal mechanical element whose force is proportional to relative acceleration, enabling it to mirror electrical impedance behavior. The inerter permits mechanical analogues of electrical circuits, allows synthesis of any positive‑real impedance with components of small mass, and shows promise for vibration absorption, suspension strut design, and simulation.

Abstract

The paper is concerned with the problem of synthesis of (passive) mechanical one-port networks. One of the main contributions of the paper is the introduction of a device, which win be called the inerter, which is the true network dual of the spring. This contrasts with the mass element which, by definition, always has one terminal connected to ground. The inerter allows electrical circuits to be translated over to mechanical ones in a completely analogous way. The inerter need not have large mass. This allows any arbitrary positive-real impedance to be synthesized mechanically using physical components which may be assumed to have small mass compared to other structures to which they may be attached. The possible application of the inerter is considered to a vibration absorption problem, a suspension strut design, and as a simulated.