Propagation of bending waves in phononic crystal thin plates with a point defect

Abstract

a b s t r a c tIn this paper, the band structures of bending waves in a phononic crystal thin plate with a point defect are studied using an improved plane wave expansion method combined with the supercell technique. In particular, a phononic crystal thin plate composed of an array of circular crystalline Al 2 O 3 cylinders embedded in an epoxy matrix with a square lattice is considered in detail. Full band gaps are shown. When a point defect is introduced, the bending waves are highly localized at or near the defect, resulting in defect modes. The frequency and number of the defect modes are strongly dependent on the filling fraction of the system and the size of the point defect. The defect bands appear from the upper edge of the gap and move to the middle of the gap as the defect size is reduced. For a given defect, the frequencies of the defect bands increase as the filling fraction increases.

Polarized pass band for longitudinal waves in solid phononic crystals

“…The band structure of the PC is influenced by many factors [19][20][21][22][23]46], and the PLPB can be modulated via geometrical parameters and/or material properties. In this section, we investigate how these factors will affect the PLPB.…”

“…PCs were first proposed to eliminate the propagation of waves owing to the band gaps [14,15]. Many investigations have been conducted since then to generate or enlarge the band gaps for practical applications [16][17][18][19][20][21][22][23][24][25][26][27][28][29]. Compared with PCs of which the periodicity is of the same order as the wavelength, AMMs are composed of subwavelength units.…”

“…, where ρ, E and ν represent mass density, Young's modulus, and Poisson ratio, respectively [23]. The inclusions are cylindrical and are periodically embedded in the matrix to form a square lattice.…”

Influence of surface stress and atomic defect generation on Rayleigh waves in laser-excited solids

“…We consider the case of harmonic waves so that the solutions ϕ , ψ and 1 n , of equations (13) and (14) take the forms of…”

“…A model of the propagation of bending elastic waves in phononic crystal thin plates with a point defect has been considered in [14]. They sown, that the frequency and number of the defect modes are strongly dependent on the filling fraction of the system and the size of the point defect.…”