Natural vibration of elastic metamaterial beam under arbitrary elastic boundary conditions

Abstract

Elastic metamaterial (EM) is a kind of new composite material/structure that provides a new feasible way of vibration control in many scenarios. Although some analytical means for solving the vibration behavior of EM components with simple shapes and classic boundary conditions (BCs) have been presented, the analyses of those with complex shapes or BCs that are common in reality remain to be studied further. In this paper, the natural vibration problem of a typical EM beam under arbitrary elastic boundary conditions (EBC) is investigated by using the effective medium theory (EMT) and the Rayleigh-Ritz method. The inherent correlations between the EM beam and corresponding modified matrix beam together with the modified static equivalent beam are disclosed for their modal behaviors. The extraordinary natural vibration properties of the EM beam under arbitrary EBC are revealed and some common features are concluded. This work may provide a useful reference for further investigations of many other similar EM structures.