Tunability of Band Gaps in Two-Dimensional Phononic Crystals with Magnetorheological and Electrorheological Composites
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ISSN 1860-2134
Tunability of Band Gaps in Two-Dimensional Phononic Crystals with Magnetorheological and Electrorheological Composites Gang Zhang1,2
Yuanwen Gao1,2
1
( Key Laboratory of Mechanics on Environment and Disaster in Western China, The Ministry of Education of China, Lanzhou University, Lanzhou 730000, China) (2 Department of Mechanics and Engineering Science, College of Civil Engineering and Mechanics, Lanzhou University, Lanzhou 730000, China)
Received 14 May 2020; revision received 7 August 2020; Accepted 24 August 2020 c The Chinese Society of Theoretical and Applied Mechanics 2020
ABSTRACT The elastic wave propagation properties of phononic crystals (PnCs) composed of an elastic matrix embedded in magnetorheological and electrorheological elastomers are studied in this paper. The tunable band gaps and transmission spectra of these materials are calculated using the finite element method and supercell technology. The variations in the band gap characteristics with changes in the electric/magnetic fields are given. The numerical results show that the electric and magnetic fields can be used in combination to adjust the band gaps effectively. The start and stop frequencies of the band gap are obviously affected by the electric field, and the band gap width is regulated more significantly by the magnetic field. The widest and highest band gap can be obtained by combined application of the electric and magnetic fields. In addition, the band gaps can be moved to the low-frequency region by drilling holes in the PnC, which can also open or close new band gaps. These results indicate the possibility of multi-physical field regulation and design optimization of the elastic wave properties of intelligent PnCs.
KEY WORDS Phononic crystal, Band gap, Magnetic field, Electric field, Combined adjustment
1. Introduction Phononic crystals (PnCs) are formed by arranging several different materials according to a specific periodic law. PnC material properties are similar to those of photonic crystals in that there are forbidden bands and elastic waves within the band gap frequency range that will not propagate in PnCs [1]. Vibration and noise are among several important indicators that affect mechanical or engineering equipment. The forbidden band characteristics of PnCs can suppress such harmful vibration and noise effectively [2–6]. One of the band gap generation mechanisms in PnCs is Bragg scattering, which requires the lattice size to be of the same order of magnitude as the wavelength of the sound waves [7]. A second mechanism that involves locally resonant phononic crystals (LRPnCs) was proposed by Liu et al. [7] in 2000. Modal analysis shows that the resonance-excited wave of the scatterer in the band gap interacts with the incident wave to suppress elastic wave propagation. Low-frequency vibration is ubiquitous in nature.
Corresponding author. E-mail: [email protected]
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LRPnCs can control large wavelength elastic waves with only a small-sized structure. This makes it possible to desig
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