טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentLustig Ben
SubjectMetamaterial Wave Phenomena in Laminates
DepartmentDepartment of Mechanical Engineering
Supervisor Assistant Professor Gal Shmuel
Full Thesis textFull thesis text - English Version


Abstract

Metamaterials are synthetic materials with properties not found in nature. Such properties are achieved by clearly arranging conventional materials in periodic patterns. Specifically, elastodynamic metamaterials are tailored to control traversing mechanical waves, through designed band gap, negative refraction and beam steering phenomena. These phenomena are useful for various applications, such as noise suppression, vibration isolation and energy tunneling.


The goal of this thesis is to study metamaterial wave phenomena in the simplest elastic periodic media ??? laminates. While wave propagation in laminates has been extensively studied since the 50's, their dynamic response has yet to be completely characterized. This thesis contains a significant study towards such characterization, as explained next. The band structure of a periodic medium describes which wave frequencies, termed gaps, it filters out, depending on the medium composition. We show in the second chapter that all the infinite band structures of multiphase laminates impinged by normal waves are remarkably encapsulated in a finite geometric object, independently of the specific laminate composition. This object establishes a platform for unprecedented characterization of the band structure. We specifically use it to rigorously determine the density of gaps in the spectrum, and proves it exhibits universal features. We further numerically study the dependency of the gap density on the impedance and number of phases. We also use the object to formulate optimization problems of the gap widths, and develop simple bounds. Finally, we show that our analysis can be applied to non-linear multiphase laminates undergoing pre-deformations.


In the third chapter we study metamaterial properties of laminates undergoing in-plane motion. In this kind of motion pressure and shear waves are coupled in a way that leads to a rich and complex behavior. We develop an analytical method to solve the governing equations and analyze this behavior. Through numerical examples we find that in-plane waves can be negatively refracted and steered for long wavelengths in simple configurations. Specifically, we realize that in comparison to pure shear waves, for which the ability to negatively refract has been demonstrated before for an impinge upon a multiple-layer interface, coupled waves are also capable of this phenomenon while impinging a simple single-layer interface. Moreover, we find exceptional points, at which eigenmodes coalesce and energy flow is extremely sensitive to the incident angle of the incoming wave. These non-Hermitian degeneracies with propagating modes, which to date were realized by balancing energy gain and loss in systems with parity-time symmetry, are reported here in a purely elastic setting. Finally, we develop an approximated method to determine the scattering coefficients of a pertinent interface problem.