A Nonlinear Damped Metamaterial: Wideband Attenuation with Nonlinear Bandgap and Modal Dissipation

TL;DR

This paper introduces a nonlinear damped metamaterial that achieves wideband vibration attenuation by combining nonlinear damping effects with locally resonant structures, expanding the capabilities of traditional linear metamaterials.

Contribution

It presents a novel design integrating nonlinear damping into locally resonant metamaterials, enabling amplitude-dependent and broader bandgap attenuation.

Findings

Bandgap is amplitude-dependent and widened.

Nonlinear damping reduces modal frequencies.

Experimental validation confirms theoretical predictions.

Abstract

In this paper, we incorporate the effect of nonlinear damping with the concept of locally resonant metamaterials to enable vibration attenuation beyond the conventional bandgap range. The proposed design combines a linear host cantilever beam and periodically distributed inertia amplifiers as nonlinear local resonators. The geometric nonlinearity induced by the inertia amplifiers causes an amplitude-dependent nonlinear damping effect. Through the implementation of both modal superposition and numerical harmonic methods the finite nonlinear metamaterial is accurately modelled. The resulting nonlinear frequency response reveals the bandgap is both amplitude-dependent and broadened. Furthermore, the modal frequencies are also attenuated due to the nonlinear damping effect. The theoretical results are validated experimentally. By embedding the nonlinear damping effect into locally resonant metamaterials, wideband attenuation of the proposed metamaterial is achieved, which opens new possibilities for versatile metamaterials beyond the limit of their linear counterparts.