Experimental and numerical study of elastic metamaterial with negative Young’s modulus model
Date Issued
2014
Date
2014
Author(s)
Yu, Jian-Syun
Abstract
This article presents methods for modeling, analysis, and design of metamaterial beams with extreme Young’s modulus. Metamaterials are man-made materials that make objects exhibit behavior different from the general laws of physics by changing the geometry and dimensions. Metamaterial research extends from the electromagnetic into acoustics and solid mechanics. By different mechanism such as translational or rotational vibration, Elastic solid metamaterials would be the equivalent models of media having negative mass density, negative Young''s modulus, or negative bulk modulus in excitation force. Objects can be made vibration absorption when utilizing those phenomena.
The thesis is divided into three parts. First, through a combination of Euler-Bernoulli beam, spring-mass system and trusses construct a theoretical model. From a unit cell of an infinite metamaterial beam (meta-beam), governing equations are derived using the extended Hamilton principle. By Bloch-Floquet theory for periodic structures we except to find the stop-band in the dispersion curve created by resonators. We uses the incoming elastic wave in the beam to resonant the spring-mass system. We expect that the system resonance creates additional bending moments to stop the wave propagation in meta-beam. Second, we design the possible practical meta-beam. The effect of the meta-beam is explicitly confirmed by analysis of wave propagation using numerical simulations in COMSOL. By numerical simulation, we expect to find the actual working mechanism in meta-beams and their transient responses. Finally, the practical designs and their dynamic behaviors are examined and discussed using numerical simulations.
Subjects
超穎材料
等效楊氏模數
尤拉樑
波傳行為
Type
thesis
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