Scattering of elastic waves by periodic arrays of spherical bodies

By I. Psarobas, N. Stefanou, A. Modinos. 2000

269 citations recorded by the source corpus.

We develop a formalism for the calculation of the frequency band structure of a phononic crystal consisting of nonoverlapping elastic spheres, characterized by Lam\'e coefficients which may be complex and frequency dependent, arranged periodically in a host medium with different mass density and Lam\'e coefficients. We view the crystal as a sequence of planes of spheres, parallel to and having the two-dimensional periodicity of a given crystallographic plane, and obtain the complex band structure of the infinite crystal associated with this plane. The method allows one to calculate, also, the transmission, reflection, and absorption coefficients for an elastic wave (longitudinal or transverse) incident, at any angle, on a slab of the crystal of finite thickness. We demonstrate the efficiency of the method by applying it to a specific example.

Subfields: Biomedical Engineering, Geophysics, Oceanography

View Paper: https://www.semanticscholar.org/paper/c1403596ec9f569c9ebacf74c2fcf54dc4767d07

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Citations in the corpus

Higher order asymptotic homogenization and wave propagation in periodic composite materials (2008, methodology): “…1997), (ii) the Korringa–Kohn–Rostoker method (also known as the multiplescattering theory, see Kafesaki & Economou (1999), Liu et al. (2000) and Psarobas et al. (2000), and (iii) the Rayleigh multipole expansions method and its generalizations (Nicorovici et al. 1995; Movchan et al. 1997,…”
Classical vibrational modes in phononic lattices: theory and experiment (2005, methodology): “The on-shell layer MS method [19, 33] can treat very”
Metamaterial-inspired structures and concepts for elastoacoustic wave energy harvesting (2013, background): “These abilities have been exploited for the design of innovative actuators and sensors, and elements of logic circuitry based on the propagation of elastic waves [30, 31].”
Efficient formulation for band-structure calculations of two-dimensional phononic-crystal plates (2006, background): “Most of the studies concerning phononic crystals focused on investigation of the bulk acoustic waves [3-7], and parts of them reported on the acoustic waves localized at the surface of two-dimensional, semi-infinite phononic crystals [8-11].”
Phononic crystals for liquid sensor applications (2009, methodology): “These include the transfer matrix method [37], the FDTD method [38–40] and the layer MST (LMST) for 2D [41] and 3D phononic crystals [31, 42, 43].”
Genetic algorithm optimization of phononic bandgap structures (2006, methodology): “…difference time domain (FDTD) method (Sigalas and Garcia, 2000; Tanaka et al., 2000; Tanaka and Tamura, 2002), the multiple scattering (MST) method (Psarobas et al., 2000; Kafesaki and Economou, 1999), and traditional finite element (FEM) methods (Mead, 1996; Zhang et al., 2003c; Axmann and…”