Simplified Timoshenko-Ehrenfest beam equation to analyze metamaterials

Abstract

This paper is devoted to the incorporation of rotary inertia and shear deformation in the study of acoustic metamaterials. An overwhelming majority of investigators resort to either Bernoulli-Euler or to the Timoshenko-Ehrenfest beam theories. Here, we demonstrate that the full version of the Timoshenko-Ehrenfest beam theory is not needed, and the truncated version is sufficient. An extensive numerical investigation is conducted to this end.