A new meta-rod attenuating low-frequency waves with external fixed supporting

Abstract

To attenuate low-frequency waves in a rod, this study proposes a new meta-rod with compression springs attached to an external fixed supporting. In particular, an essential problem concerns how external constraints on the negative-stiffness system influence the bandgap properties and wave attenuation behaviour explored. We analytically derive the dispersion relation of the meta-rod and reveal its bandgap properties using the transfer matrix method. Then we develop a finite-length meta-rod model and investigate its wave attenuation behaviour by the finite element method. By attaching compression springs to an external fixed supporting, the bandgap is shifted to cover the lower frequencies range with deep wave attenuation. Furthermore, the local resonance bandgap and the Bragg bandgap are effectively coupled by tuning the stiffness of the compression springs to obtain a wider bandgap. We envision the proposed meta-rod can be used as an effective countermeasure to mitigate vibrations at low frequencies.