Investigation of Elastic Meta-Structures With Periodic Localized Stress-Fields

Abstract

Elastic meta-structures, with wave propagation control capabilities, have been widely investigated for mechanical vibrations suppression and acoustics attenuation applications. Periodic architected lattices, combined with mechanical or electromechanical resonators, are utilized to form frequency bands over which the propagation of elastic waves is forbidden, known as bandgaps. The characteristics of these bandgaps, in terms of frequency range and bandwidth, are determined by the local resonators as well as characteristics of the individual cells out of which the structure is composed. In this study, the effectiveness of local stress fields as a tool for bandgap tuning in active, elastic meta-structures is investigated. A finite beam undergoing axial and flexural deformations, with a spatially periodic axial loads acting on it, is chosen to demonstrate the concept. The beam is first divided into several sections where localized stress-fields are varied periodically. Lateral and longitudinal deformations of the beam are described, respectively, by the Timoshenko beam theory and the Elementary rod theory. The Frequency-domain Spectral Element Method is then employed to calculate the forced-vibration response of the structure. The effects of the local state-of-stress on the width and frequency of the resulting bandgaps are investigated.