Forced vibrations of a finite length metabeam with periodically arranged internal hinges and external supports

Abstract

The paper investigates a problem of forced vibrations of two finite length metabeams: one is with periodically arranged internal hinges and the second one with periodically arranged internal hinges and external supports. Based on the Euler–Bernoulli beam theory and the transfer matrix method, general solutions of the periodic beams are obtained. Applying the Bloch-Floquet theory, the explicit expressions are derived defining the metabeams band gap structures. The corresponding band gap dispersion curves are plotted and analysed. It is shown that when the frequency of forced vibrations coincides with the band gap frequencies a strong localization of flexible waves occurs at the interfaces of the periodic beams. The localization of flexible waves increases significantly with the number of hinges and supports.