New and Old Formulas from the Helmholtz Equation with Half-Space Driving Sources

2021 ◽  
pp. 65-76
Author(s):  
Martin Ochmann ◽  
Rafael Piscoya
Keyword(s):  
Helmholtz Equation ◽  
Half Space

The Helmholtz equation with impedance in a half-space

2005 ◽  
Vol 341 (9) ◽  
pp. 561-566 ◽  
Author(s):  
Mario Durán ◽  
Ignacio Muga ◽  
Jean-Claude Nédélec
Keyword(s):  
Helmholtz Equation ◽  
Half Space

scholarly journals Dynamic analysis of a cylindrical cavity in inhomogeneous elastic half-space subjected to SH waves

2017 ◽  
Vol 24 (1) ◽  
pp. 299-311 ◽  
Author(s):  
Zailin Yang ◽  
Guanxixi Jiang ◽  
Haiyi Tang ◽  
Baitao Sun ◽  
Yong Yang
Keyword(s):  
Stress Concentration ◽  
Helmholtz Equation ◽  
Half Space ◽  
Cylindrical Cavity ◽  
Variable Coefficient ◽  
Dynamic Stress ◽  
Dynamic Stress Concentration ◽  
Mapping Technique ◽  
Concentration Factors ◽  
Stress Concentration Factors

Based on complex function methods and a multipolar coordinate system, the scattering induced by a cylindrical cavity in a radially inhomogeneous half-space is investigated. Mass density of the half-space varies depending on the distance from the centre of the cavity while the shear modulus is always constant. The wave velocity is expressed as a function of radius vector and the Helmholtz equation is a partial differential equation with a variable coefficient. By means of a conformal mapping technique, the Helmholtz equation with a variable coefficient is transferred into its normal form. Then, displacement fields and corresponding stress components are deduced. Applying the boundary conditions, dynamic stress concentration factors around the cavity are obtained and analyzed. Typical numerical results are presented to demonstrate the distribution of dynamic stress concentration factors when influencing parameters are assumed.

A SIMPLE METHOD FOR COMPUTING THE GREEN FUNCTIONS OF THE HELMHOLTZ EQUATION IN THE TWO-DIMENSIONAL IMPEDANCE HALF SPACE

2010 ◽  
Vol 18 (01) ◽  
pp. 1-11 ◽  
Author(s):  
Z.-S. CHEN ◽  
H. WAUBKE
Keyword(s):  
Helmholtz Equation ◽  
Half Space ◽  
Numerical Experiments ◽  
Green Functions ◽  
Two Dimensional ◽  
Simple Method

Green functions of Helmholtz's equation in an impedance half space (IHS) can be computed using various methods, e.g. the method presented by S. N. Chandler-Wilde and D. C. Hothersall.1 The approach of W. L. Li, T. W. Wu and A. F. Seybert2 is simpler, but it can only be used in a mass-like IHS. In this paper, the method is reformulated so that it can also be used in a stiffness-like IHS. Numerical experiments indicate that the method yields reliable results.

The Helmholtz Equation in a Locally Perturbed Half-Space with Non-Absorbing Boundary

2008 ◽  
Vol 191 (1) ◽  
pp. 143-172 ◽  
Author(s):  
Mario Durán ◽  
Ignacio Muga ◽  
Jean-Claude Nédélec
Keyword(s):  
Helmholtz Equation ◽  
Half Space ◽  
Absorbing Boundary

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.

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