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Dynamics of Phononic Materials and Structures: Historical Origins, Recent Progress, and Future Outlook

The Journal of the Acoustical Society of America

Two-dimensional phononic crystals: Examples and applications

A chiral elastic metamaterial beam for broadband vibration suppression

The lumped-mass method is applied to study the propagation of elastic waves in two-dimensional binary periodic systems, i.e., periodic soft rubber/epoxy and vacuum/epoxy composites, for which the conventional methods fail or converge very slowly. A comprehensive study is performed for the two-dimensional binary locally resonant phononic crystals, which are composed of periodic soft rubber cylinders immersed in epoxy host. Numerical simulations predict that subfrequency gaps also appear because of the high contrast of mass density and elastic constant of the soft rubber. The locally resonant mechanism in forming the subfrequency gaps is thoroughly analyzed by studying the two-dimensional model and its quasi-one-dimensional mechanical analog. The rule used to judge whether a resonant mode in the phononic crystals can result in a corresponding subfrequency gap or not is found.

Two-dimensional locally resonant phononic crystals with binary structures.

Flexural vibration in Timoshenko beams with periodically attached local resonators is studied theoretically and experimentally. The existence of a low frequency flexural vibration gap is indicated by the complex band structure calculated with transfer matrix theory for an infinite beam, as well as the frequency response function calculated with the finite element method for a finite Timoshenko beam with finite local resonators. This finite Timoshenko beam was manufactured and vibration experiments generated an experimental frequency response function curve showing a vibration gap as expected. The existence of low frequency gaps in Timoshenko beams with local resonators provides a method of flexural vibration control of beams.

Flexural vibration band gaps in Timoshenko beams with locally resonant structures

Using the transfer matrix theory, we provided the band structure of flexural waves in an Euler-Bernoulli beam with locally resonant structures, with two degrees of freedom, i.e., a resonator with vertical and rotational vibration. The frequency response function of a finite periodic system was calculated by the finite element method. The material damping of rubber makes the gaps wider in the calculation. These theoretical results show a good agreement with those of the experiment. The measured result provides an attenuation of over $20\phantom{\rule{0.3em}{0ex}}\mathrm{dB}$ in the frequency range of the band gaps. The existence of low-frequency band gaps in such a beam provides a method of flexural vibration control of beams.

Flexural vibration band gaps in Euler-Bernoulli beams with locally resonant structures with two degrees of freedom

One-dimensional phononic crystals with locally resonant structures

In this paper, we present a design of locally resonant (LR) beams using periodic arrays of beam-like resonators (or beam-like vibration absorbers) attached to a thin homogeneous beam. The main purpose of this work is twofold: (i) providing a theoretical characterization of the proposed LR beams, including the band gap behavior of infinite systems and the vibration transmittance of finite structures, and (ii) providing experimental evidence of the associated band gap properties, especially the coexistence of LR and Bragg band gaps, and their evolution with tuned local resonance. For the first purpose, an analytical method based on the spectral element formulations is presented, and then an in-depth numerical study is performed to examine the band gap effects. In particular, explicit formulas are provided to enable an exact calculation of band gaps and an approximate prediction of band gap edges. For the second purpose, we fabricate several LR beam specimens by mounting 16 equally spaced resonators onto a free-free host beam. These specimens use the same host beam, but the resonance frequencies of the resonators on each beam are different. We further measure the vibration transmittances of these specimens, which give evidence of three interesting band gap phenomena: (i) transition between LR and Bragg band gaps; (ii) near-coupling effect of the local resonance and Bragg scattering; and (iii) resonance frequency of local resonators outside of the LR band gap. [DOI: 10.1115/1.4024214]

Gang Wang

Papers

Two-dimensional locally resonant phononic crystals with binary structures.

Flexural vibration band gaps in Timoshenko beams with locally resonant structures

Flexural vibration band gaps in Euler-Bernoulli beams with locally resonant structures with two degrees of freedom

One-dimensional phononic crystals with locally resonant structures

Theoretical and Experimental Study of Locally Resonant and Bragg Band Gaps in Flexural Beams Carrying Periodic Arrays of Beam-Like Resonators