Eventos Anais de eventos
COBEM 2023
27th International Congress of Mechanical Engineering
Numerical Investigation on the Dynamic Behaviour of 1-D Hierarchical Mechanical Metamaterials
Submission Author:
Edson Jansen Pedrosa de Miranda Junior , MA
Co-Authors:
CASSIO BRUNO FLORENCIO GOMES, Antonio Vinicius Garcia Campos, Edilson Dantas Nóbrega, Flavio Nunes Pereira, Jose Maria Campos dos Santos, Edson Jansen Pedrosa de Miranda Junior
Presenter: CASSIO BRUNO FLORENCIO GOMES
doi://10.26678/ABCM.COBEM2023.COB2023-0841
Abstract
Metamateriais are artificial structures designed to achieve performance over static or dynamic conditions that usual materials would not be able to accomplish. In mechanical structures, they are applied for noise control, vibration isolation and wave attenuation, for example. Some reliable mathematical models are available to simulate and analyse the behaviour of structures over dynamic conditions, then it is possible to reach and validate accurate results without necessarily performing experiments. Recently, the effect of hierarchy has been combined to the convenient properties offered by mechanical metamaterials. In this work, the complex dispersion diagram and the forced response of flexural waves propagating in a 1-D hierarchical metamaterial Euler-Bernoulli beam are investigated. The influence of graded arrays of spring-mass resonators attached to the surface of a homogeneous beam on the formation of Bragg-type and locally resonant band gaps is studied. The hierarchy has been placed at the mass, stiffness and position of the resonators, as well as the combination of these parameters, for example, both position and stiffness of resonators following a specific pattern. Cases with different number of resonators were also evaluated, i.e. single resonator and multiple resonators attached to the beam. The plane wave expansion (PWE), extended plane wave expansion (EPWE), wave spectral element (WSE), and wave finite element (WFE) approaches are used to compute the complex dispersion diagram of the hierarchical metamaterial beam with attached resonators. The forced response is computed by the spectral element (SE), WSE, and WFE approaches. The numerical results of all methods present good agreement. It was possible to identify band gaps for the studied structures, as well as analyse and compare different types of hierarchy (mass, position or these two combined) and how it influences the wave propagation through the structure. Additionally, the hierarchy can improve both unit cell wave attenuation and vibration reduction of the metamaterial beam.
Keywords
Metamaterials, wave propagation, graded structures, frequency response function, band gaps
