Stress-optimized inertial amplified metastructure with opposite chirality for vibration attenuation

TL;DR

This paper introduces a novel inertial amplified metastructure with opposite chirality that enables wide-band vibration attenuation, supported by analytical, numerical, and experimental validation, and optimized for minimal bandgap frequency and structural integrity.

Contribution

It presents a new chirality-based metastructure design with analytical and experimental validation, and an optimization framework for vibration attenuation applications.

Findings

Supports a tunable attenuation zone controlled by coupled modes

Laboratory measurements confirm wide-band filtering properties

Optimized design minimizes bandgap frequency while ensuring structural safety

Abstract

In this work, we investigate the dynamics and attenuation properties of a one-dimensional inertial amplified lattice with opposite chirality. The unit cell of the structure consists of a hollow-square plate connected to a ring through arch-like ligaments. The peculiar geometry and orientation of the links allow for coupling the axial and the torsional motion of the lattice, thus amplifying the inertia of the system. We develop both simplified analytical and numerical models of the building block to derive the complex dispersion relation of the infinite lattice. The structure supports a frequency-tailorable attenuation zone, whose lower bound is controlled by the second coupled axial-torsional mode. Laboratory measurements of the transmission spectrum on a 3D printed sample match very well with the analytical and numerical predictions, confirming the wide-band filtering properties of this lattice. We complete our investigation by developing and solving a constrained optimization model to obtain the optimized geometric parameters of the unit cell that minimize the bandgap opening frequency and, at the same time, fulfill structural requirements. In particular, the internal stresses induced by the self-weight of the structure are kept to a low by virtue of the employed design, with the aim to prevent plastic deformations and failure. The inertial amplification mechanism, proposed and investigated in this work, offers an efficient variant for the efficient design of materials and structures for vibration mitigation and shock protection.