Flexural Wave Bandgaps in a Prestressed Multisupported Timoshenko Beam with Periodic Inerter-Based Dynamic Vibration Absorbers

Abstract

Locally resonant (LR) metamaterial structures possess bandgaps in which wave propagation is significantly attenuated. In this paper, we discuss flexural wave bandgaps in an LR beam subjected to a global axial force and multiple vertical elastic supports. An array of inerter-based dynamic vibration absorbers (IDVAs) was periodically attached to the LR beam. The flexural wave band structure of this prestressed multisupported LR beam was first derived using the transfer matrix method (TMM) and then explicitly illustrated through a numerical example. Four bandgaps were identified: a bandgap located in the low-frequency zone, a Bragg band generated by Bragg scattering, and two LR bands generated by the local resonance of the IDVAs. The effects of the IDVA parameters, axial force, and vertical elastic support on the properties of the bandgaps were evaluated. In particular, the bandgaps merged accompanied by an exchange of their edge frequencies. The bandwidth of the merged bandgap was nearly equal to the sum of the bandwidths of the bandgaps involved, indicating a method for controlling broadband flexural vibration through the bandgap splicing mechanism.