Direct and Inverse Wave Propagation in the Frequency Domain via the Weyl Operator Symbol Calculus

1995 ◽  
Author(s):  
Louis Fishman
Keyword(s):  
Wave Propagation ◽  
Weyl Operator ◽  
Symbol Calculus ◽  
Reflection And Transmission ◽  
First Order ◽  
Wave Propagation Problem ◽  
Phase Space Methods ◽  
Matrix Characteristic ◽  
Operator Symbols ◽  
Reflection And Transmission Operators

Abstract Wave field splitting, invariant imbedding, and phase space methods reformulate the Helmholtz wave propagation problem in terms of an operator scattering matrix characteristic of the modeled environment. The equations for the reflection and transmission operators are first-order in range, nonlinear (Riccati-like), and, in general, nonlocal. The singularity structure of the corresponding Weyl operator symbols plays a crucial role in the development of both direct and inverse wave propagation algorithms.

Wave Propagation Simulation in Damaged Isotropic and Anisotropic Solids Using K-Space Method

2018 ◽  
Vol 26 (04) ◽  
pp. 1850023
Author(s):  
Qinan Chang ◽  
Tishun Peng ◽  
Yongming Liu
Keyword(s):  
Wave Propagation ◽  
First Order ◽  
Inverse Fourier Transformation ◽  
Wave Propagation Problem ◽  
Convergence Study ◽  
The Time Domain ◽  
Pseudo Spectral Method ◽  
Pseudo Spectral ◽  
Space Method ◽  
First Order Differential Equations

A numerical model for wave propagation simulation in damaged isotropic and anisotropic solids is proposed in this paper. The wave propagation problem is formulated using two coupled first-order differential equations for both isotropic and anisotropic solids, and a wavenumber corrector-based pseudo-spectral method is used to obtain the time-domain solution using the forward and inverse Fourier transformation. Following this, explicit modeling of crack-like damage commonly seen in engineering materials is investigated. Parametric and convergence study is performed to investigate the proposed simulation algorithms. Numerical examples are used to verify the proposed methodology by comparing the results from analytical solutions and classical finite element methods. Discussions and conclusions are drawn based on the proposed study.

On a technique for deriving explicit transfer matrices of orthotropic layers

2015 ◽  
Vol 37 (4) ◽  
pp. 303-315 ◽  
Author(s):  
Pham Chi Vinh ◽  
Nguyen Thi Khanh Linh ◽  
Vu Thi Ngoc Anh
Keyword(s):  
Wave Propagation ◽  
Explicit Form ◽  
Half Space ◽  
Transfer Matrix ◽  
Rayleigh Waves ◽  
Secular Equation ◽  
Transfer Matrices ◽  
Orthotropic Layer ◽  
Wave Propagation Problem ◽  
Arbitrary Thickness

This paper presents  a technique by which the transfer matrix in explicit form of an orthotropic layer can be easily obtained. This transfer matrix is applicable for both the wave propagation problem and the reflection/transmission problem. The obtained transfer matrix is then employed to derive the explicit secular equation of Rayleigh waves propagating in an orthotropic half-space coated by an orthotropic layer of arbitrary thickness.

scholarly journals Micro-Vibrations and Wave Propagation in Biperiodic Cylindrical Shells

2020 ◽  
Vol 22 (3) ◽  
pp. 789-808
Author(s):  
Barbara Tomczyk ◽  
Anna Litawska
Keyword(s):  
Wave Propagation ◽  
Periodic Structures ◽  
Cylindrical Shells ◽  
Combined Model ◽  
Asymptotic Models ◽  
Wave Propagation Problem ◽  
Modelling Procedure ◽  
Constant Coefficients ◽  
A Cell ◽  
Averaged Model

AbstractThe objects of consideration are thin linearly elastic Kirchhoff-Love-type circular cylindrical shells having a periodically microheterogeneous structure in circumferential and axial directions (biperiodic shells). The aim of this contribution is to study a certain long wave propagation problem related to micro-fluctuations of displacement field caused by a periodic structure of the shells. This micro-dynamic problem will be analysed in the framework of a certain mathematical averaged model derived by means of the combined modelling procedure. The combined modelling applied here includes two techniques: the asymptotic modelling procedure and a certain extended version of the known tolerance non-asymptotic modelling technique based on a new notion of weakly slowly-varying function. Both these procedures are conjugated with themselves under special conditions. Contrary to the starting exact shell equations with highly oscillating, non-continuous and periodic coefficients, governing equations of the averaged combined model have constant coefficients depending also on a cell size. It will be shown that the micro-periodic heterogeneity of the shells leads to exponential micro-vibrations and to exponential waves as well as to dispersion effects, which cannot be analysed in the framework of the asymptotic models commonly used for investigations of vibrations and wave propagation in the periodic structures.

Generalization of von Neumann analysis for a model of two discrete half-spaces: The acoustic case

Geophysics ◽  
2007 ◽  
Vol 72 (5) ◽  
pp. SM35-SM46 ◽  
Author(s):  
Matthew M. Haney
Keyword(s):  
Wave Propagation ◽  
Numerical Model ◽  
Finite Difference ◽  
Stability Criterion ◽  
Reflection And Transmission Coefficients ◽  
Reflection And Transmission ◽  
Von Neumann ◽  
Transmission Coefficients ◽  
Strong Material ◽  
Von Neumann Analysis

Evaluating the performance of finite-difference algorithms typically uses a technique known as von Neumann analysis. For a given algorithm, application of the technique yields both a dispersion relation valid for the discrete time-space grid and a mathematical condition for stability. In practice, a major shortcoming of conventional von Neumann analysis is that it can be applied only to an idealized numerical model — that of an infinite, homogeneous whole space. Experience has shown that numerical instabilities often arise in finite-difference simulations of wave propagation at interfaces with strong material contrasts. These interface instabilities occur even though the conventional von Neumann stability criterion may be satisfied at each point of the numerical model. To address this issue, I generalize von Neumann analysis for a model of two half-spaces. I perform the analysis for the case of acoustic wave propagation using a standard staggered-grid finite-difference numerical scheme. By deriving expressions for the discrete reflection and transmission coefficients, I study under what conditions the discrete reflection and transmission coefficients become unbounded. I find that instabilities encountered in numerical modeling near interfaces with strong material contrasts are linked to these cases and develop a modified stability criterion that takes into account the resulting instabilities. I test and verify the stability criterion by executing a finite-difference algorithm under conditions predicted to be stable and unstable.

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