Deterministic interface modes in two-dimensional acoustic systems

The interface state in two-dimensional (2D) sonic crystals (SCs) was obtained based on trying or cutting approach, which greatly limits its practical applications. In this paper, we theoretically demonstrate that one category of interface states can deterministically exist at the boundary of two square-lattice SCs due to the geometric phase transitions of bulk bands. First, we derive a tight-binding formalism for acoustic waves and introduce it into the 2D case. Furthermore, the extended 2D Zak phase is employed to characterize the topological phase transitions of bulk bands. Moreover, the topological interface states can be deterministically found in the nontrivial bandgap. Finally, two kinds of SCs with the [Formula: see text] symmetry closely resembling the 2D Su–Schrieffer–Heeger (SSH) model are proposed to realize the deterministic interface states. We find that tuning the strength of intermolecular coupling by contacting or expanding the scatterers can effectively induce the bulk band inversion between the trivial and nontrivial crystals. The presence of acoustic interface states for both cases is further demonstrated. These deterministic interface states in 2D acoustic systems will be a great candidate for future waveguide applications.

Explicit coupling of acoustic and elastic wave propagation in finite-difference simulations

We present a mechanism to explicitly couple the finite-difference discretizations of 2D acoustic and isotropic elastic-wave systems that are separated by straight interfaces. Such coupled simulations allow for the application of the elastic model to geological regions that are of special interest for seismic exploration studies (e.g., the areas surrounding salt bodies), with the computationally more tractable acoustic model still being applied in the background regions. Specifically, the acoustic wave system is expressed in terms of velocity and pressure while the elastic wave system is expressed in terms of velocity and stress. Both systems are posed in first-order forms and are discretized on staggered grids. Special variants of the standard finite-difference operators, namely, operators that possess the summation-by-parts property, are used for the approximation of spatial derivatives. Penalty terms, which are also referred to as the simultaneous approximation terms, are designed to weakly impose the elastic-acoustic interface conditions in the finite-difference discretizations and couple the elastic and acoustic wave simulations together. With the presented mechanism, we are able to perform the coupled elastic-acoustic wave simulations stably and accurately. Moreover, it is shown that the energy-conserving property in the continuous systems can be preserved in the discretized systems with carefully designed penalty terms.

Applying Incompatible Meshes for Modeling Structural-Acoustic Domains in Energy Finite Element Analysis

The Energy Finite Element Analysis (EFEA) has been developed for modeling coupled structural-acoustic systems at mid-to-high frequencies when conventional finite element methods are no longer computationally efficient because they require very fine meshes. In standard Finite Element Analysis (FEA) approach, governing differential equations are formulated in terms of displacements which vary harmonically with space. This requires larger numbers of elements at higher frequencies when wavelengths become smaller. In the EFEA, governing differential equations are formulated in terms of energy density that is spatially averaged over a wavelength and time averaged over a period. The resulting solutions vary exponentially with space which makes them smooth and allows for using much coarser meshes. However, current EFEA formulations require exact matching between the meshes at the boundaries between structural and acoustic domains. This creates practical inconveniences in applying the method as well as limits its use to only fully compatible meshes. In this paper, a new formulation is presented that allows for using incompatible meshes in EFEA modeling, when shapes and/or sizes of elements at structural-acoustic interfaces do not match. In the main EFEA procedure, joints formulations between structural and acoustic domains have been changed in order to deal with non-matching elements. In addition, the new Pre-EFEA procedure which allows for automatic searching and formation of the new types of joints is developed for models with incompatible meshes. The new method is tested using a spherical shaped structural-acoustic interface. Results for incompatible meshes are validated by comparing to solutions obtained using regular compatible meshes. The effects of mesh incompatibility on the accuracy of results are discussed.