Propagation of waves and vibrations in hyperbolic elastic metamaterials

• Grant number: 23/05972-2
• Support Opportunities: Scholarships in Brazil - Doctorate (Direct)
• Start date: August 01, 2023
• End date: May 31, 2026
• Field of knowledge: Engineering - Mechanical Engineering - Mechanics of Solids
• Principal Investigator: José Roberto de França Arruda
• Grantee: Carolyne Beatriz Simões Valentin
• Host Institution: Faculdade de Engenharia Mecânica (FEM). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 18/15894-0 - Periodic structure design and optimization for enhanced vibroacoustic performance: ENVIBRO, AP.TEM

Abstract

Mechanical vibrations are caused by the propagation of waves in an elastic solid. It is important to be able to control the vibrations and channel them where they do not cause problems or where they can be recovered in energy harvesting processes. Elastic metamaterials are structures, usually periodic or quasi-periodic, whose geometry and composition make them behave in a way not commonly found in conventional materials such as metals and polymers. The concept was initially formulated for electromagnetic waves and later applied to elastic waves in solids and acoustic waves in fluids. Periodic structures are generally studied from their unit cell, to which boundary conditions corresponding to an infinite periodic structure are applied. These boundary conditions are called Bloch-Floquets, a theory used in the solution of differential equations with periodic coefficients. This theory demonstrates that the solution of these equations has a periodic nucleus of the same period as the coefficients and a propagation term characterized by a wave number that represents the propagation in the periodic medium. The behavior of this vector wavenumber as a function of frequency is called the dispersion ratio. Scatter diagrams allow investigating wave propagation in periodic media, indicating, for example, frequency bands in which elastic waves propagate (pass bands) or do not propagate (gap bands). In this research, two types of elastic metamaterials will be investigated, the so-called hyperbolic metamaterials (in which the isofrequency lines of the scatter diagram describe hyperbolas) and the hyperbolic geometry metamaterials (in which the periodicity is distorted when projected onto a hyperbolic surface). Hyperbolic metamaterials were initially proposed and investigated in relation to the propagation of electromagnetic waves. More recently, the behavior of elastic hyperbolic metamaterials, which have unusual topological behaviors, has been studied. Topological behaviors have the virtue of being robust to imperfections and defects caused by manufacturing processes. On the other hand, designing periodicities in non-Euclidean geometries opens new possibilities for the design of metastructures with unknown properties in conventional periodic elastic media. Such behaviors may find application in vibration and noise control, for example in land and aerospace vehicles. For this purpose, analytical and numerical methods of wave propagation analysis, such as the plane wave superposition method (PWE) and the wave finite element method (WFE), and numerical analysis of the dynamic behavior of structures, such as the finite element method (FEM) and the spectral element method (SEM), will be used. (AU)