Band structure analysis of leaky Bloch waves in 2D phononic crystal plates

Abstract

A hybrid Finite Element-Plane Wave Expansion method is presented for the band structure analysis of phononic crystal plates with two dimensional lattice that are in contact with acoustic half-spaces. The method enables the computation of both real (propagative) and imaginary (attenuation) components of the Bloch wavenumber at any given frequency.Three numerical applications are presented: a benchmark dispersion analysis for an oil-loaded Titanium isotropic plate, the band structure analysis of a waterloaded Tungsten slab with square cylindrical cavities and a phononic crystal plate composed of Aurum cylinders embedded in an epoxy matrix.

Hierarchical large-scale elastic metamaterials for passive seismic wave mitigation

“…Once this sorting rule is applied, the diagrams can be simplified, selecting only SAW modes, as shown in Figure 3B and E. Some of the dispersion curves are not continuous along the whole Brillouin path G À X because they undergo a transformation from true-SAWs to pseudo-SAWs (i.e., waves propagating with exponential attenuation, due to energy leakage into the bulk), as detailed in [20,21]. Figure 3A and D also reports the longitudinal and shear bulk wave velocities as dashed black and red lines, respectively.…”

Modeling Bloch Waves in Prestressed Phononic Crystal Plates

“…Due to the periodicity of the system under consideration, in the undeformed configuration C 0 any scalar, vector or tensor function φ satisfies the condition φ(x 0 + r 0 m) = φ(x 0 ), where m ∈ Z 2 and r 0 = [r 01 , r 02 ] is the matrix of lattice vectors. This allows to restrict the computational domain to a unit cell of domain 0 and boundary ∂ 0 (Collet et al, 2011;Mazzotti et al, 2017). Similarly, the unit cell in the configuration C satisfies the periodic condition φ…”

A high-quality narrow passband filter for elastic SV waves via aligned parallel separated thin polymethylmethacrylate plates

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