By taking a two-dimensional solid local resonant phononic crystal as an example, we investigated the mechanism of the defect state on a subwavelength scale. It is well known that, when the working wavelength is much greater than the distance between resonators, the dispersion of the phononic crystal is insensitive to the lattice structure, and the whole structure can be described in terms of the effective medium theory. As a result, it is hard to introduce a defect state in the system by a local real-space disorder. It is shown in this paper that the dispersion of the local resonant phononic crystal can be understood from the long-range feature of the interaction between resonators, so the creation of a defect state in the system is in fact to break such a long-range interaction. Based on this understanding, the mechanisms of the recently reported methods, that are used to create defect states, are discussed. In addition, a waveguide structure that can guide the longitude or transverse waves separately is realized by introducing an anisotropic defect resonator.
Taking the flexural wave propagating in elastic thin plate as an example, we investigate the mechanism for gap opening in the resonator-based acoustic metamaterials. Results show that the band gap in such a kind of structure depends not only on the abrupt phase change of the wave when it is scattered by the resonators, but also on the retarded phase of wave when it is propagating in host. This means that the dispersion of wave in the structure can be adjusted either by the scattering or by the propagating phase. Based on this understanding, we show that the defect state at subwavelength scale (obtained either by changing locally the resonating property of the resonator or by changing locally the distance between the resonators) can be understood simply by the band gap condition. We show further in this paper that, because the dispersion of the metamaterial can be adjusted by the propagating phase, the structures with negative band at a subwavelength scale can also be achieved by arranging the resonators into a compound lattice.
In this paper, by taking the acoustic property of a two-dimensional squarely arranged Helmholtz resonator array for example, we point out that there exist two kinds of couplings in the local resonance phononic crystal, which are the coupling between the resonator and background and the coupling among the resonators, respectively. The first coupling effect can be changed by changing the quality factor of the resonator. A local-resonant type of band gap can be converted into a Bragg-scattering type continually when this kind of coupling becomes larger and larger. The second one, which is based on the overlapping of the near filed around the resonators, can be enhanced by reducing the distance between the nearest resonators. As a result, a wider band gap, but a smaller penetration depth of the wave, can be obtained.
Using the plane-wave expansion method, we study the band structure of a phononic crystal with water rods embedded in mercury to form a super-cell according to the two-dimensional Fibonacci array. It is found that each band splits into three sub-bands with the change of quasilattice constants and there exist intermediate states, which reflect the peculiar properties of quasiperiodic systems.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.