Guided elastic waves and perfectly matched layers

Elastic waveguides support propagating modes that have two possible features, negative group velocities and long wavelengths that, for some frequencies, degrade the accuracy or otherwise poison existing numerical schemes that utilise perfectly matched layers (PMLs) to mimic infinite domains. We illustrate why negative group velocities and long waves are potentially an issue and describe how these problems are overcome. Detailed numerical simulations confirm the accuracy of the modified scheme and provide both theoretical and pragmatic estimates for the parameters within the PML model, in particular for the damping function. We also contrast and compare different implementations of the PML model using spectral and finite difference methods.     

A facile method to realize perfectly matched layers for elastic waves

In perfectly matched layer (PML) technique, an artificial layer is introduced in the simulation of wave propagation as a boundary condition which absorbs all incident waves without any reflection. Such a layer is generally thought to be unrealizable due to its complicated material formulation. In this paper, on the basis of transformation elastodynamics and complex coordinate transformation, a novel method is proposed to design PMLs for elastic waves. By applying the conformal transformation technique, the proposed PML is formulated in terms of conventional constitutive parameters and then can be easily realized by functionally graded viscoelastic materials. We perform numerical simulations to validate the material realization and performance of this PML.     

Existence of backward propagating acoustic waves in supported layers

Conditions for the existence of acoustic waveguide modes with the direction of the group velocity opposite to that of the phase velocity in supported layers are investigated. We begin with a study of a clamped-free layer and show that the occurrence of the negative slope in the dispersion of the second and higher order modes leading to backward propagation is a commonly encountered phenomenon related to accidental degeneracies between longitudinal and transverse thickness resonances. For a layer on an elastic substrate, the negative dispersion slope exists only when the transverse velocity of the layer is very small compared to that of the substrate, which makes backward propagation a rarely occurring phenomenon in real structures. Finally, we explain how mode-crossing in certain bi-layer structures results in the negative slope in the dispersion of the fundamental mode.     

Numerical interaction of boundary waves with perfectly matched layers in two space dimensional elastic waveguides

Perfectly matched layers (PMLs) are now a standard approach to simulate the absorption of waves in open domains. Wave propagation in elastic waveguides has the possibility to support back-propagating modes (propagating modes with oppositely directed group and phase velocities) with long wavelengths. Back-propagating modes can lead to temporally growing solutions in the PML. In this paper, we demonstrate that back-propagating modes in a two space dimensional isotropic elastic waveguide are not harmful to a discrete and finite width PML. Analysis and numerical experiments confirm the accuracy and stability of the PML.     

Hardy space infinite elements for time-harmonic two-dimensional elastic waveguide problems

We consider time-harmonic linear elasticity equations in domains containing two-dimensional semi-infinite strips. Since for such problems there exist modes with different signs of group and phase velocity, standard perfectly matched layer (PML) as well as standard Hardy space infinite element methods fail.We apply a recently developed infinite element method for a physically correct discretization of such waveguide problems which is based on a Laplace transform in propagation direction. In the Laplace domain the space of transformed solutions can be separated into a sum of a space of incoming and a space of outgoing functions where both function spaces are certain Hardy spaces. The Hardy space is chosen such that the construction of a simple infinite element is possible.The method does not use a modal separation and works on domains of frequencies. On those domains the involved operators are frequency independent and hence lead to linear eigenvalue problems when computing resonances. Numerical experiments containing convergence tests and resonance problems are included.     

On the existence of non-polarized azimuthal-symmetric electromagnetic waves in circular dielectric waveguide filled with nonlinear isotropic homogeneous medium

The propagation of monochromatic nonlinear symmetric hybrid waves in a cylindrical nonlinear dielectric waveguide is considered. The physical problem is reduced to solving a transmission eigenvalue problem for a system of ordinary differential equations. Spectral parameters of the problem are propagation constants of the waveguide. The problem is reduced to the new type of nonlinear eigenvalue problem. The analytical method of solving this problem is presented. New propagation regime is found.