Séminaires du
Département
d'Acoustique Physique
Institut de Mécanique et d'Ingénierie
Université de Bordeaux - UMR CNRS 5295
Alexander Darinskii
Institute of Crystallography, Russian Academy of Sciences, Moscow
Vendredi 24 janvier 2014
11 h 00
Salle de conférences RdC A4
FEM simulation of the acoustic wave propagation in
phononic crystals and half-infinite anisotropic
substrates
The application of the finite element method (FEM) to the simulation of the
harmonic bulk and surface acoustic wave propagation is discussed. Numerical
computations of coordinate dependent fields are carried out within a spatially
bounded domain. In this regard a task is definite if the structure under study is fully
bounded by natural borders. Such a case is exemplified by computations of the
spectrum of a 2D-phononic crystal (PC). This 2D periodic structure is formed of
identical solid rods immersed into water parallel to one another. Accordingly, the
computational domain is the unit cell. Of our interest are points of the 1st Brillouin
zone, where the frequency degeneracy occurs, and features of the pressure
distribution over the unit cell related with this degeneracy.
A more involved situation is met when a 2D-structure is periodic only along one
direction. As examples of the simulation of the wave propagation in 1D-periodic 2Dstructures, we discuss the FE procedures of finding the reflection and transmission
coefficients of a bulk wave incident on a PC plate immersed into water, as well as of
computing the spectrum of modes supported by a waveguide created in a PC plate.
We also discuss the use of FEM for the simulation of the surface and leaky wave
propagation in the infinite periodic gratings created on the surface of half-infinite
piezoelectric substrate. In all these cases, the eigenfunction expansion is used to
represent the wave fields outside the computational domain.
A third situation is the simulation of the wave propagation in a 2D-structure without
any periodicity and either unbounded or not fully bounded by natural borders. In this
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case it is required to truncate the computational domain by virtual borders in a way
excluding the appearance of “parasitic” wave fields. A possible method is the
implementation of the perfectly matched layer (PML). We briefly review the basic
idea underlying the PML method and afterwards consider the application of FEM in
conjunction with the PML method to the investigation of the surface acoustic wave
scattering from single imperfections and gratings of finite length on the surface of
half-infinite isotropic and anisotropic substrates.