Waves in elastically coupled sandwich beams: An analytical investigation

Abstract

Flexural wave propagation through a sandwich beam, composed of two parallel Euler–Bernoulli beams connected with the translational and rotational springs at a periodic interval (acronym metasandwich), is analytically investigated in this paper. Dimensionless governing parameters are obtained by non-dimensionalizing the governing differential equations. Band structure of the metasandwich has been obtained by implementing Bloch's theorem in conjunction with the transfer matrix. The two parallel beams are modeled separately, which demonstrated the key novelty of the paper. A new band categorization criteria of the wave phenomena in metasandwich is proposed within the scope of this paper. Furthermore, an exploration of the parametric space has also been conducted to observe the variation of the band structure. The underlying physics of the wave propagation or attenuation in the different bands are conceptualized from its respective mode shapes and energy plots. The similarity between the mode shapes of the parallel beams has been analyzed by using cross recurrence plots.