Wave localization in randomly disordered layered three-component phononic crystals with thermal effects

Abstract

In this paper, the propagation and localization of elastic waves in randomly disordered layered threecomponent phononic crystals with thermal effects are studied. The transfer matrix is obtained by applying the continuity conditions between three consecutive sub-cells. Based on the transfer matrix method and Bloch theory, the expressions of the localization factor and dispersion relation are presented. The relation between the localization factors and dispersion curves is discussed. Numerical simulations are performed to investigate the influences of the incident angle on band structures of ordered phononic crystals. For the randomly disordered ones, disorders of structural thickness ratios and Lamé constants are considered. The incident angles, disorder degrees, thickness ratios, Lamé constants and temperature changes have prominent effects on wave localization phenomena in three-component systems. Furthermore, it can be observed that stopbands locate in very low-frequency regions. The localization factor is an effective way to investigate randomly disordered phononic crystals in which the band structure cannot be described.

Modulation of the Band Gaps of Phononic Crystals with Thermal Effects

“…The two layers are lead and epoxy materials and denoted by A and B, respectively. The materials constants can be found in [11,14] and are listed in Table 1.The wave velocity of the incident wave,c, is taken as 800 m·s −1 .The angle of the incidence is taken as θ 0 = 10 • , and the temperature is considered as T = 20 • C. Since the structure is considered as inhomogeneous structure, the dispersive characteristics are determined by the ratios of materials properties. Hence, we consider the thickness ratio of each material ζ 1 :ζ 2 is 1:1.…”

“…Based on the Bloch theorem and Floquet's theorem, due to the periodicity of the layered component PnCs, the displacement and stress at the boundaries between two neighboring unit cells satisfy the following relations [11,14]:…”

“…Assume that the PnCs consist of n unit cells, the boundary conditions at the left and right sides of the two layers in the ith unit cell are written as [11] ϕ (i)…”

“…For the case of SH-waves polarized in the z-direction propagating in the x y-plane, the governing equation in each material (layer) can be written in the following form [10][11][12].…”

Wave Propagation in Nanoscaled Periodic Layered Structures

“…[30][31][32][33][34][35][36][37][38] Recently, some results for wave propagation in the 1D randomly disordered and quasi-periodic PNCs were also presented. [39][40][41][42] With the rapid development of the technology in the fields of communication information, medical engineering, etc., the size of acoustic devices is required to be smaller and smaller. For instance, the gigahertz communication generally requires the nanosized devices.…”