Biaxial flexural wave propagation in asymmetric & periodic Euler-Bernoulli beam

Abstract This research deals with the study of biaxial flexural wave propagation through asymmetric and periodic beams which is underexplored in the literature. It proposes a novel analytical formulation for the analysis of biaxial flexural wave propagation in a periodic beam type metamaterial with periodicity of the principal directions using Bloch theorem considering Euler–Bernoulli beam assumption. Through the proposed formulation principal directions of wave propagation and corresponding propagation and attenuation factors at each frequency are obtained. Frequency response function (FRF) obtained through both 1D and 3D finite element analysis (FEA) for the asymmetric periodic Euler–Bernoulli beam (APEB) is used to validate the analytical solution. A satisfactory agreement between stop and pass bands obtained from our proposed formulation, 1D and 3D FEA is observed. A detailed parametric study is also carried out to analyse the effect of parameters like geometry, cross sectional orientations and material properties on the wave propagation characteristics. Apart from full stop bands where waves corresponding to both the principal directions attenuate or don’t propagate, possibility of creating partial stop bands where waves corresponding to one principal direction propagate and corresponding to other principal direction attenuate or don’t propagate is also observed. Relative orientation of consecutive spans (i.e., subunits) is found to have significant impact on width and location of both partial and full stop bands. Adding more different orientations of the principal direction within a unit cell is observed to produce more stop bands, both full and partial, providing another pathway for tuning wave propagation in metamaterials beams.