Realization of 2D bandgap with dimensional expansion of flexural metamaterial

Abstract

Vibration-related issues are crucial consideration in various industries. Most vibrational phenomena are closely associated with flexural wave that vibrates along a transverse axis and propagates along structures such as plates and beams. Accordingly, studies on flexural metamaterials aimed at controlling flexural waves for the purpose of vibration isolation has been consistently conducted recently. Metamaterial is structures in which artificial shapes smaller than the wavelength of propagating waves are periodically arranged. Through such structures, it’s possible to control the propagation of the wave in a new way different from the general way. There are various phenomena caused by these metamaterials, such as negative refraction, non-reciprocity, band gap, wave localization, and more. In this thesis, bandgap, the most representative phenomenon among those cause by metamaterials, was utilized to block flexural waves in a specific frequency band on x-y plane. Previous studies on flexural metamaterials have been mainly conducted in one dimension, and the Timoshenko beam theory, which considers the shear deformation of the structure, converts a continuous beam into a mass-spring system with two degrees of freedom of shear and bending motions. Thus, broadband vibration isolation is implemented at low frequencies. However, in these studies, only waves in the x-direction can be controlled. Therefore, in this thesis, we extend the existing one-dimensional flexural metamaterial to two dimensions and convert the plate into a mass-spring system with three degrees of freedom by additionally considering the torsional motion rotating along the y-axis in addition to the existing shear and bending motions. As the degree of freedom is added, the frequency components that make up the band gap in the dispersion curve change, and conditions for forming a two-dimensional band gap are added accordingly. In this thesis, two-dimensional bandgap formation was achieved through the design of a unit cell with shear stiffness, bending stiffness, and torsional stiffness that satisfies the conditions, and it was verified through numerical analysis and experiments that waves do not propagate in all direction in the bandgap. Through the research conducted in this thesis, it became possible to block flexural waves in all directions in a two-dimensional structure, and it is expected that flexural metamaterials will be able to effectively block vibrations in plates.