Flexural Waves in Elastically Coupled Telescopic Metabeams

Abstract

This paper investigates the flexural wave propagation through elastically coupled telescopic metabeams. It is assumed that the metabeam is formed by connecting successive beams with each other using distributed elastic springs. The equations of motion of a representative unit of the above-mentioned novel structural form are established by dividing it into three constitutive components that are two side beams, modeled employing the Euler–Bernoulli beam equation and an elastically coupled articulated distributed spring connection (ECADSC) at middle. ECADSC is modeled as parallel double beams connected by distributed springs. The underlying mechanics of this system in context of elastic wave propagation is unique when compared with the existing state of art in which local resonators, inertial amplifiers, etc. are attached to the beam to widen the attenuation bandwidth. The dynamic stiffness matrix is employed in conjunction with Bloch–Floquet theorem to derive the band structure of the system. It is identified that the coupling coefficient of the distributed spring layer and length ratio between the side beams and the elastic coupling plays the key role in the wave attenuation. It has been perceived that a considerable widening of the attenuation bandgap in the low frequency can be achieved while the elastically distributed springs are weak and distributed in a small stretch. Specifically, 140% normalized bandgap can be obtained only by tuning the stiffness and the length ratio without adding any added masses or resonators to the structure.