Time-harmonic waves in viscoelastic media

1989 ◽  
Vol 16 (1) ◽  
pp. 53-58 ◽  
Author(s):  
Giacomo Caviglia ◽  
Angelo Morro ◽  
Enrico Pagani
Keyword(s):  
Harmonic Waves ◽  
Viscoelastic Media ◽  
Time Harmonic

Numerical Simulation of Time-Harmonic Waves in Inhomogeneous Media using Compact High Order Schemes

2011 ◽  
Vol 9 (3) ◽  
pp. 520-541 ◽  
Author(s):  
Steven Britt ◽  
Semyon Tsynkov ◽  
Eli Turkel
Keyword(s):  
Fourth Order ◽  
Finite Difference Methods ◽  
Accurate Method ◽  
Variable Coefficients ◽  
High Order ◽  
Harmonic Waves ◽  
Order Convergence ◽  
High Order Schemes ◽  
Time Harmonic ◽  
Difference Methods

AbstractIn many problems, one wishes to solve the Helmholtz equation with variable coefficients within the Laplacian-like term and use a high order accurate method (e.g., fourth order accurate) to alleviate the points-per-wavelength constraint by reducing the dispersion errors. The variation of coefficients in the equation may be due to an inhomogeneous medium and/or non-Cartesian coordinates. This renders existing fourth order finite difference methods inapplicable. We develop a new compact scheme that is provably fourth order accurate even for these problems. We present numerical results that corroborate the fourth order convergence rate for several model problems.

Guided Circumferential Waves in a Circular Annulus

1998 ◽  
Vol 65 (2) ◽  
pp. 424-430 ◽  
Author(s):  
Guoli Liu ◽  
Jianmin Qu
Keyword(s):  
Frequency Dispersion ◽  
Radius Of Curvature ◽  
Harmonic Waves ◽  
Two Dimensional ◽  
Numerical Examples ◽  
Circular Annulus ◽  
Time Harmonic ◽  
Steady State Time ◽  
Wave Phenomena ◽  
Circumferential Waves

A two-dimensional circular annulus is considered in this paper as a waveguide. The guided steady-state time-harmonic waves propagating in the circumferential direction are studied. It is found that the guided circumferential waves are dispersive. The dispersion equation is derived analytically and numerical examples are presented for the frequency dispersion curves. The displacement profiles across the wall thickness of the annulus are also obtained for the first five propagating modes. In addition, the analogy between a flat plate and an annulus in the asymptotic limit of infinite radius of curvature is discussed to reveal some interesting wave phenomena intrinsic to curved waveguides.

scholarly journals METASURFACE SYNTHESIS FOR TIME-HARMONIC WAVES: EXACT SPECTRAL AND SPATIAL METHODS (Invited Paper)

2014 ◽  
Vol 149 ◽  
pp. 205-216 ◽  
Author(s):  
Mohamed A. Salem ◽  
Karim Achouri ◽  
Christophe Caloz
Keyword(s):  
Harmonic Waves ◽  
Spatial Methods ◽  
Time Harmonic

Elastic Waves in Inhomogeneous Elastic Media

1972 ◽  
Vol 39 (3) ◽  
pp. 696-702 ◽  
Author(s):  
Adnan H. Nayfeh ◽  
Siavouche Nemat-Nasser
Keyword(s):  
Perturbation Method ◽  
Incident Wave ◽  
Elastic Waves ◽  
Harmonic Waves ◽  
Elastic Media ◽  
Time Harmonic ◽  
Special Cases ◽  
Inhomogeneous Elastic Media ◽  
Inhomogeneous Elastic Medium ◽  
Large Frequency

The WKB solution is derived together with the condition for its validity for elastic waves propagating into an inhomogeneous elastic medium. Large frequency expansion solution is also derived. It is found that the WKB solution agrees with that derived for large frequencies when the frequency approaches infinity. Some exact solutions are deduced from the WKB solution. Finally, we consider motions in medium which consists of a material with harmonic periodicity. The solution is obtained by means of a perturbation method. It is shown that, only when the wavelength of the incident wave is small compared with the periodicity-length of the material, the WKB solution constitutes a good approximation. When the wavelength is comparable with this periodicity-length, then, in certain special cases, the material cannot maintain time-harmonic waves; such harmonic waves are not “stable.” These and other solutions are discussed in detail.

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