Natural vibration analysis of an embedded elastic metamaterial beam based on effective medium theory and Rayleigh–Ritz method

Abstract

Elastic metamaterial (EM) beam is a kind of special composite structure with peculiar dynamic properties that are beneficial for relevant vibration isolating applications. The vibration properties and proper analysis methods of these special structures are the main concerns in practical designs and analyses. Existing analytic methods can only be applied to a few cases with simple geometric shapes and boundary conditions, hence more general analysis means are needed to be developed. In this paper, a general analysis method is proposed by combining the effective medium theory (EMT) and Rayleigh–Ritz method. Based on the method, the natural vibration properties of a typical EM beam are revealed clearly and correctly, such as absence of natural frequencies within bandgap, gathering of natural frequencies in the vicinity of band edges and particular modal correspondence before and behind bandgap. The effectiveness of the proposed method is validated by the analysis results, thus providing a feasible way for analyzing many complex cases where EM beams are included.