Dynamic behaviour of elastic metamaterial system with negative effective mass and modulus

Abstract

Elastic metamaterials have received growing attention from the research community due to their unique properties and attractive engineering applications. The unusual elastic wave manipulation ability of the elastic metamaterials mainly comes from the delicately designed structural configuration. This thesis aims to developing elastic metamaterial systems with engineered representative cell featuring negative effective mass and/or modulus, and then conduct a systematic investigation of their dynamic behaviour, as well as their interesting applications. To investigate the underlying mechanism of generating negative effective parameters, a two-dimensional elastic metamaterial model, consisting of a series of properly arranged rigid bodies and linear springs, is developed to exhibit both negative effective mass and modulus under specific frequencies. In this model, the translational resonance of the resonators can generate negative effective mass by inducing overall motion of the representative cells, whereas the translational resonance can generate negative effective modulus through giving rise to the local deformation of the representative cells without overall motion. By generating such controllable translational and rotational resonances in the representative cell, negative effective mass and modulus can be achieved independently. The effect of the generated negative effective mass and/or modulus on wave propagation of the elastic metamaterial has been studied. Then, from this design strategy, a new one-dimensional elastic metamaterial is designed to possess negative effective mass and/or modulus through two types of local translational resonance introduced in the representative cell, to avoid the potential difficulties in fabrication associated with rotational motion. The unique feature of the representative cell endows the elastic metamaterial model with great flexibility to generate these two negative effective parameters in different frequency ranges, the independent control of which is realized to some extent. Numerical analysis has been conducted to show its strong wave mitigation ability with single negative effective parameter and the phenomenon of negative phase velocity is observed when simultaneously negative effective mass and modulus exist. Based on the one-dimensional elastic metamaterial, a new two-dimensional elastic metamaterial model is developed with simultaneously negative effective mass density, bulk modulus and shear modulus. Analytical study of the new metamaterial system is performed based on a simplified model to study the effect of the main material and geometric parameters. Numerical analysis is further conducted to simulate wave propagation in the current metamaterial. The results show that this new elastic metamaterial can behave like solid with negative phase velocities for longitudinal and transverse waves and also can behave like fluid mainly supporting longitudinal waves with negative phase velocities. For the new two-dimensional metamaterial designed, numerical analysis is performed to further study the wave propagation in the metamaterial system containing a large number of periodically distributed material cells. The phenomenon of negative refraction is observed at the frequency with negative phase velocity, which can potentially be utilized for sub-wavelength imaging. The numerical results clearly show the wave blocking ability of the anisotropic model in broad frequency ranges, which can be applied in vibration isolation and noise reduction. The elastic metamaterial models and the investigations presented in this thesis shed new light on the design strategy of elastic metamaterials with negative effective parameters and provide insights into developing such metamaterials with various special functionalities.