Related papers: Converging bounds for the effective shear speed in…
The quasistatic limit of the antiplane shear-wave speed ('effective speed') $c$ in 2D periodic lattices is studied. Two new closed-form estimates of $c$ are derived by employing two different analytical approaches. The first proceeds from a…
A new formula for the effective quasistatic speed of sound $c$ in 2D and 3D periodic materials is reported. The approach uses a monodromy-matrix operator to enable direct integration in one of the coordinates and exponentially fast…
Effective elastic moduli for 3D solid-solid phononic crystals of arbitrary anisotropy and oblique lattice structure are formulated analytically using the plane-wave expansion (PWE) method and the recently proposed monodromy-matrix (MM)…
Existence of shear horizontal (SH) surface waves in 2D-periodic phononic crystals with an asymmetric depth-dependent profile is theoretically reported. Examples of dispersion spectra with band gaps for subsonic and supersonic SH surface…
In this paper the salient features of the Plane Wave Expansion (PWE) method and the mixed variational technique are combined for the fast eigenvalue computations of arbitrarily complex phononic unit cells. This is done by expanding the…
The refraction properties of phononic crystals are revealed by examining the anti-plane shear waves in doubly periodic elastic composites with unit cells containing rectangular and/or elliptical inclusions. The band-structure, group…
A two dimensional flat phononic crystal (PC) lens for focusing off-plane shear waves is proposed. The lens consists of a triangular lattice hole-array, embedded in solid matrix. Self-collimation effect is employed to guide the shear waves…
Two-dimensional (2D) photonic crystals offer strong control over the propagation of light through their bands. Theoretical methods for computing the band structure in 2D are well-established and fast because 2D photonic crystals are…
Two-dimensional ternary locally resonant phononic crystals used to consist of cylindrical scatterers with uniform coatings in their exterior. An alternative coating scheme with a comblike profile is proposed and investigated in this letter.…
It is shown, for the first time, that negative refraction with positive phase velocity refraction can be realized (and controlled) over a wide range of frequency on the first (lowest) pass band of simple photonic and phononic crystals.…
We present a new method, in the following called MMM2D, to accurately calculate the electrostatic energy and forces on charges being distributed in a two dimensional periodic array of finite thickness. It is not based on an Ewald summation…
The surface-impedance matrix method is used to study interfacial waves polarized in a plane of symmetry of anisotropic elastic materials. Although the corresponding Stroh polynomial is a quartic, it turns out to be analytically solvable in…
The propagation of acoustic or elastic waves in artificial crystals, including the case of phononic and sonic crystals, is inherently anisotropic. As is known from the theory of periodic composites, anisotropy is directly dictated by the…
In this paper we present a comprehensive study on the multi-objective optimization of two-dimensional porous phononic crystals (PnCs) in both square and triangular lattices with the reduced topology symmetry of the unit-cell. The fast…
We present a comprehensive method for determining {both exact and approximate} dispersion {relations} for one-dimensional {resonant phononic} crystals, applicable to a wide range of structures, regardless of their specific characteristics.…
The paper extends the formulation of a 2D geometrically exact beam element proposed in our previous paper [1] to curved elastic beams. This formulation is based on equilibrium equations in their integrated form, combined with the kinematic…
Consider the approximation of stochastic Allen-Cahn-type equations (i.e. $1+1$-dimensional space-time white noise-driven stochastic PDEs with polynomial nonlinearities $F$ such that $F(\pm \infty)=\mp \infty$) by a fully discrete space-time…
Today's standard fabrication processes are just capable of manufacturing slab of photonic and phononic crystals, so an efficient method for analysis of these crystals is indispensable. Plane wave expansion (PWE) as a widely used method in…
Shear to longitudinal mode conversion via second harmonic generation is studied theoretically and computationally for plane waves in a two-dimensional, adhesive, hexagonally close-packed microscale granular medium. The model includes…
A new method for Ewald summation in planar/slablike geometry, i.e. systems where periodicity applies in two dimensions and the last dimension is "free" (2P), is presented. We employ a spectral representation in terms of both Fourier series…