Phononic materials act as mechanical filters of incident acoustic and vibrational loads. Generally speaking, they attenuate wave propagation within bandgaps and resonate outside them. Nonetheless, elastic periodic lattices often exhibit “truncation resonances” inside bandgaps when certain conditions are met. This study provides a generalized roadmap for the design and selective placement of truncation resonances in such lattices, integrating all factors that play a role in the onset of truncation resonances and shape its dynamic response. This framework is then experimentally validated using a canonical physical realization of differently-truncated finite phononic lattices.
This work presents an effort to understand the evolution of Bragg scattering band gaps in the context of the transfer functions of finite Phononic Crystals (PCs). Following the dispersion analysis of an infinite PC based on a single unit cell, an analytical derivation of the natural frequencies of a finite PC with a given number of cells is presented. Next, the transfer function between the tip displacement of a finite PC and a force exerted at the other end is derived in closed-form, and used to establish an understanding of the band gap formation in the finite setting. The analysis reveals that the phenomenon can be attributed to the split of poles around the center of the band gap and the absence of any poles within it. The formation mechanism is then discussed in light of several numerical examples with different combinations of system parameters and number of cells.
Considerable research attention has been recently devoted to the study of periodic structures given their unique wave dispersion. Phononic crystals and acoustic metamaterials have emerged as two main categories of such periodic structures that can exhibit radically different band gap characteristics. Here, we present a novel configuration that combines hybrid wave attenuation attributes culminating in enhanced metadamping and energy dissipation properties. The results are compared with a benchmark example from literature to show the potential of the new design.
KEYWORDS: Metamaterials, Wave propagation, Algorithm development, Acoustics, Resonators, Finite element methods, Aluminum, Signal attenuation, Barium, Systems modeling, Control systems design
Elastic metamaterials are sub-wavelength structures with locally resonant components that contribute to the rise of tunable stop bands, i.e. frequency ranges within which waves do not propagate. A new approach is presented here to quantify this stop band behavior by evaluating structural vibrational power in the different constituents of locally resonant metamaterials undergoing axial excitations. It is shown that the power flow patterns match wave propagation information extracted from the dispersion analysis of the metamaterial unit cell, and can thus be used to develop an algorithm that numerically predicts stop band frequencies for finite realizations with given dimensions and a known number of cells.
Internal resonators in lumped spring-mass elastic metamaterials reveal unique wave dispersion characteristics. Using the Bloch-wave analysis and the Transfer Matrix Method (TMM), the band structure of a unit cell of a locally resonant metamaterial shows a band gap (region of near-perfect wave attenuation) despite the lack of any damping elements. This paper presents an analytical closed-form model of a finite metamaterial structure comprising a chain of unit cells to try to understand the band gap behavior. The poles and zeros of the derived transfer functions explain the formation mechanism of the band gap and ties the band structure predictions of the single cell to the structural dynamics of the resultant metamaterial.
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