Phononic band gaps in two-dimensional periodic structures with inertial amplification mechanisms

Abstract

In this thesis, a 2D periodic structure equipped with inertial amplification mechanisms is designed. The structure is optimized to obtain a wide and deep phononic band gap in low frequency ranges. The aim is to prevent wave propagation, hence suppress mechanical vibrations. In the literature, there are two common ways to generate band gaps, Bragg scattering and resonance scattering. Alternative to these methods, inertial amplification method is used in this study. Different types of inertial amplification mechanisms are discussed. Then, a 1D distributed parameter model, which is equivalent to the proposed inertial amplification mechanism is used to construct the 2D periodic structure. First two natural frequencies of the 1D model are found analytically. The model is designed to have a band gap between these two natural frequencies. Yet, in order to calculate the frequencies more accurately, and easily optimize the model, Finite Element Analysis is conducted on the model. The 2D periodic structure is composed of two different 1D unit models. These models are optimized so that the 2D structure has a wide and deep band gap at low frequencies. Prototypes of the two 1D unit models and the 2D structure are produced, and frequency responses of them are obtained by experimental modal analysis. The experimental and numerical frequency response results match quite well, which validate that the 2D structure has a wide and deep band gap.