Anisotropic Perfectly Matched Layers for Elastic Waves in Cartesian and Curvilinear Coordinates

We develop new numerical anisotropic perfectly matched layer (PML) boundaries for elastic waves in Cartesian, cylindrical and spherical coordinate systems. The elasticity tensor of this absorbing boundary is chosen to be anisotropic and complex so that waves from the computational domain are attenuated in the boundary layer without reflection. The new PMLs are easy to formulate for both isotropic and anisotropic solid media. They utilize fewer unknowns in a general three-dimensional problem than the existing elastic wave PMLs using the field splitting scheme. Moreover, it can be implemented directly to the finite element method (FEM), as well as the finite difference time domain (FDTD) method. The high efficiency of these PMLs is illustrated by some numerical samples in FEM.Massachusetts Institute of Technology. Earth Resources LaboratoryUnited States. National Aeronautics and Space Administration (Grant #NAG3-2147)Massachusetts Institute of Technology. Borehole Acoustics and Logging Consortiu

A Simple Multi-Directional Absorbing Layer Method to Simulate Elastic Wave Propagation in Unbounded Domains

The numerical analysis of elastic wave propagation in unbounded media may be difficult due to spurious waves reflected at the model artificial boundaries. This point is critical for the analysis of wave propagation in heterogeneous or layered solids. Various techniques such as Absorbing Boundary Conditions, infinite elements or Absorbing Boundary Layers (e.g. Perfectly Matched Layers) lead to an important reduction of such spurious reflections. In this paper, a simple absorbing layer method is proposed: it is based on a Rayleigh/Caughey damping formulation which is often already available in existing Finite Element softwares. The principle of the Caughey Absorbing Layer Method is first presented (including a rheological interpretation). The efficiency of the method is then shown through 1D Finite Element simulations considering homogeneous and heterogeneous damping in the absorbing layer. 2D models are considered afterwards to assess the efficiency of the absorbing layer method for various wave types and incidences. A comparison with the PML method is first performed for pure P-waves and the method is shown to be reliable in a more complex 2D case involving various wave types and incidences. It may thus be used for various types of problems involving elastic waves (e.g. machine vibrations, seismic waves, etc)

Experimental study on damping of flexural waves in rectangular plates by means of one-dimensional acoustic 'Black Holes'

In this paper we present some recent experimental results on new lightweight and broad-band damping treatment for rectangular plates based on the so-called acoustic ‘black hole’ effect [1-5], which represents one of the most efficient ways of creating graded impedance interfaces [6] to reduce edge reflections of flexural waves. These acoustic black holes, or vibration 'traps', use elastic wedges of variable thickness defined by a power-law relationship h(x) = ε·xm (with m ≥ 2) to reduce edge reflections. In the ideal case of no edge truncations, bending wave velocities decrease to zero in such a way that the waves never reach the end and hence do not reflect back. They thus represent one-dimensional acoustic ‘black holes’ for flexural waves. It was predicted [2,3] that very low values of reflection coefficient can be achieved even in the presence of truncations and imperfections when a narrow layer of absorbing material is attached to its surface in order to dissipate the remaining energy (note that direct application of thin layers of absorbing materials to the surfaces of rectangular plates has a negligible influence on damping, which has also been demonstrated during the tests). (Continues...

Sound absorption and reflection with coupled tubes

This paper describes a special sound absorbing technique with an accompanying efficient numerical design tool. As a basis pressure waves in a single narrow tube or pore are considered. In such a tube the viscosity and the thermal conductivity of the air, or any other fluid, can have a significant effect on the wave propagation. An important aspect is that due to the viscothermal wave propagation sound energy is being dissipated. This has been applied to configurations consisting of a manifold of tubes, the so-called coupled tubes. A design strategy was developed to create broadband sound absorption for a wall with configurations of coupled tubes. The viscothermal wave propagation in tubes is accounted for in B2000 via one-dimensional T2.VISC and T3.VISC elements. Also further applications of coupled tubes are described: a network of small coupled tubes is used as a numerical representation of conventional sound absorbing material and increased damping of flexible plates connected to a small air layer is created with tubes coupled to this air layer