Three-dimensional acoustic scattering by layered media: A novel surface formulation with operator expansions implementation

2011 ◽  
Vol 130 (4) ◽  
pp. 2359-2359
Author(s):  
David Nicholls
Keyword(s):  
Three Dimensional ◽  
Acoustic Scattering ◽  
Layered Media ◽  
Operator Expansions

scholarly journals Three-dimensional acoustic scattering by layered media: a novel surface formulation with operator expansions implementation

2011 ◽  
Vol 468 (2139) ◽  
pp. 731-758 ◽  
Author(s):  
David P. Nicholls
Keyword(s):  
Acoustic Waves ◽  
Three Dimensional ◽  
Acoustic Scattering ◽  
Boundary Integral ◽  
Helmholtz Equations ◽  
Irregular Structures ◽  
Wide Range ◽  
Order Of Magnitude ◽  
Boundary Integral Operators ◽  
Operator Expansions

The scattering of acoustic waves by irregular structures plays an important role in a wide range of problems of scientific and technological interest. This contribution focuses on the rapid and highly accurate numerical approximation of solutions of Helmholtz equations coupled across irregular periodic interfaces meant to model acoustic waves incident upon a multi-layered medium. We describe not only a novel surface formulation for the problem in terms of boundary integral operators (Dirichlet–Neumann operators), but also a Boundary Perturbation methodology (the Method of Operator Expansions) for its numerical simulation. The method requires only the discretization of the layer interfaces (so that the number of unknowns is an order of magnitude smaller than volumetric approaches), while it avoids not only the need for specialized quadrature rules but also the dense linear systems characteristic of Boundary Integral/Element Methods. The approach is a generalization to multiple layers of Malcolm & Nicholls' Operator Expansions algorithm for dielectric structures with two layers. As with this precursor, this approach is efficient and spectrally accurate.

Fundamentals of generalized rigidity matrices for multi-layered media

1983 ◽  
Vol 73 (3) ◽  
pp. 749-763
Author(s):  
Maurice A. Biot
Keyword(s):  
Plane Strain ◽  
Initial Stress ◽  
Three Dimensional ◽  
Layered Media ◽  
Mathematical Structure ◽  
Irreversible Thermodynamics ◽  
Initial Stresses ◽  
General Context ◽  
Viscoelastic Media ◽  
Linear Irreversible Thermodynamics

abstract Rigidity matrices for multi-layered media are derived for isotropic and orthotropic layers by a simple direct procedure which brings to light their fundamental mathematical structure. The method was introduced many years ago by the author in the more general context of dynamics and stability of multi-layers under initial stress. Other earlier results are also briefly recalled such as the derivation of three-dimensional solutions from plane strain modes, the effect of initial stresses, gravity, and couple stresses for thinly laminated layers. The extension of the same mathematical structure and symmetry to viscoelastic media is valid as a consequence of fundamental principles in linear irreversible thermodynamics.

Adaptivity and Three Dimensional Hierarchical Boundary Elements for Rigid Acoustic Scattering Problems

1995 ◽  
Author(s):  
Steven J. Newhouse ◽  
Ian C. Mathews
Keyword(s):  
Boundary Element ◽  
Acoustic Analysis ◽  
Three Dimensional ◽  
Acoustic Scattering ◽  
Error Estimator ◽  
Infinite Domain ◽  
Scattering Problems ◽  
Effective Form ◽  
Mesh Density ◽  
Acoustic Scattering Problems

Abstract The boundary element method is an established numerical tool for the analysis of acoustic pressure fields in an infinite domain. There is currently no well established method of estimating the surface pressure error distribution for an arbitrary three dimensional body. Hierarchical shape functions have been used as a highly effective form of p refinement in many finite and boundary element applications. Their ability to be used as an error estimator in acoustic analysis has never been fully exploited. This paper studies the influence of mesh density and interpolation order on several acoustic scattering problems. A hierarchical error estimator is implemented and its effectiveness verified against the spherical problem. A coarse cylindrical mesh is then refined using the new error estimator until the solution has converged. The effectiveness of this analysis is shown by comparing the error indicators derived during the analysis to the solution generated from a very fine cylindrical mesh.

Three-Dimensional Finite Element Analysis of Elastic-Plastic Layered Media Under Thermomechanical Surface Loading

2002 ◽  
Vol 125 (1) ◽  
pp. 52-59 ◽  
Author(s):  
N. Ye ◽  
K. Komvopoulos
Keyword(s):  
Finite Element ◽  
Layered Medium ◽  
Numerical Solutions ◽  
Equivalent Stress ◽  
Three Dimensional ◽  
Layered Media ◽  
Thin Layers ◽  
Surface Loading ◽  
Elastic Plastic ◽  
Thermomechanical Surface

The simultaneous effects of mechanical and thermal surface loadings on the deformation of layered media were analyzed with the finite element method. A three-dimensional model of an elastic sphere sliding over an elastic-plastic layered medium was developed and validated by comparing finite element results with analytical and numerical solutions for the stresses and temperature distribution at the surface of an elastic homogeneous half-space. The evolution of deformation in the layered medium due to thermomechanical surface loading is interpreted in light of the dependence of temperature, von Mises equivalent stress, first principal stress, and equivalent plastic strain on the layer thickness, Peclet number, and sliding distance. The propensity for plastic flow and microcracking in the layered medium is discussed in terms of the thickness and thermal properties of the layer, sliding speed, medium compliance, and normal load. It is shown that frictional shear traction and thermal loading promote stress intensification and plasticity, especially in the case of relatively thin layers exhibiting low thermal conductivity.

Direct Simulation of Acoustic Scattering by Two- and Three-Dimensional Bodies

2000 ◽  
Vol 37 (1) ◽  
pp. 68-75 ◽  
Author(s):  
Olivier A. Laik ◽  
Philip J. Morris
Keyword(s):  
Three Dimensional ◽  
Acoustic Scattering ◽  
Direct Simulation
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