Tailoring Elastic Wave based on Nonlinearity-dependent Tunable Bandgap of Metamaterials

Abstract

As a molecule, the smallest identifiable unit with property of substance, manifests the inherent properties of material depending on how atoms are composited, metamaterials are also designed to show many physical phenomena depending on how their small unit cells are arranged in the macroscopic world. Metamaterials include a rational design with special intent of designer by defining the effective parameters which often become zero or negative. Over the last decades, metamaterials have led great attention due to their extraordinary phenomena such as negative density, negative stiffness, negative Poisson’s ratio, and negative refraction. Especially, a bandgap which can attenuate a wave propagation depending on the frequency by controlling the negative density or stiffness is one of the most widely used phenomena of the metamaterial in the mechanical engineering since the bandgap has high potential to overcome the current limit of vibration or noise problems. Recently, the advent of the more practical metamaterial, tunable metamaterials by the nonlinearity have emerged. Since the nonlinearity is determined by amplitude of incident wave, the bandgap of the nonlinear metamaterials has amplitude-dependent behavior. Although the mplitude-dependency has been investigated through the previous research on the nonlinear bandgap, the tunable bandgap by the nonlinear metamaterials has still limit to be used in practical way. In this dissertation, considering the practical use of bandgap tunability for the elastic wave, the study on the nonlinear metamaterials is shown with separation of the high frequency ultrasonic range and the low frequency vibrational range. First, for the high frequency ultrasonic range, to uncover what happens to the nonlinear bandgap as the amplitude continues to increase, a new type of bandgap, named here as “amplitude-induced bandgap” was reported in this dissertation. By starting on the theoretical dispersion of the nonlinear softening monoatomic chain, the condition for amplitude-induced bandgap was derived. Also, to support amplitude-induced bandgap and its accompanying phenomena, change in amplitude dependency, dual wavevector, and inflection point, the time transient numerical simulations were carried out. Second, for the low frequency vibration range, to realize the nonlinear tunable bandgap with practical usage, a nonlinear metamaterial with tunable bandgap at extremely low frequency is proposed and validated. Focusing on the enhancement of feasibility, the nonlinearity of the proposed metamaterial is achieved by the only linear springs. And to realize this proposed feasible metamaterial, the theoretical validation by introducing the effective mass theory, the numerical validation through finite element analysis on commercial software, and finally the vibrational experiment for the proposed metamaterial were carried out. Through the investigation of this dissertation, elastic wave tailoring with nonlinear tunability for the whole frequency range is completed. This research also paves way to harness the nonlinear metamaterials by enriching the practical usability.