Perturbation method to solve the couple problem among harmonic waves

1988 ◽  
Vol 9 (11) ◽  
pp. 1039-1044
Author(s):  
Gao Shi-qiao ◽  
Loo Wen-da
Keyword(s):  
Perturbation Method ◽  
Couple Problem ◽  
Harmonic Waves

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.

scholarly journals Homotopy Perturbation Method and Variational Iteration Method for Harmonic Waves Propagation in Nonlinear Magneto-Thermoelasticity with Rotation

2012 ◽  
Vol 2012 ◽  
pp. 1-30 ◽  
Author(s):  
Khaled A. Gepreel ◽  
S. M. Abo-Dahab ◽  
T. A. Nofal
Keyword(s):  
Perturbation Method ◽  
Iteration Method ◽  
Homotopy Perturbation Method ◽  
Variational Iteration Method ◽  
Elastic Half Space ◽  
Harmonic Waves ◽  
Variational Iteration ◽  
Homotopy Perturbation ◽  
Waves Propagation ◽  
The Difference

The homotopy perturbation method and variational iteration method are applied to obtain the approximate solution of the harmonic waves propagation in a nonlinear magneto-thermoelasticity under influence of rotation. The problem is solved in one-dimensional elastic half-space model subjected initially to a prescribed harmonic displacement and the temperature of the medium. The displacement and temperature are calculated for the methods with the variations of the magnetic field and the rotation. The results obtained are displayed graphically to show the influences of the new parameters and the difference between the methods' technique. It is obvious that the homotopy perturbation method is more effective and powerful than the variational iteration method.

Attenuation of Harmonic Waves in Layered Media

1973 ◽  
Vol 40 (1) ◽  
pp. 155-160 ◽  
Author(s):  
R. M. Christensen
Keyword(s):  
Perturbation Method ◽  
Explicit Formula ◽  
Layered Media ◽  
Harmonic Waves ◽  
Elastic Media ◽  
Attenuation Effect ◽  
The Media ◽  
The Waves ◽  
Periodic Spacing ◽  
Layered Elastic Media

The effective attenuation of harmonic waves propagating through periodically layered elastic media is studied. The waves are taken to be propagating in the direction normal to that of the layering of the media, which has alternate layers of like material. The main restriction of the derivation is that the wavelength of the waves must be long compared with the periodic spacing of the layering. An explicit formula for the attenuation is derived by a perturbation method of analysis. The analysis reveals the basic cause of the attenuation effect in terms of the scattering properties of the medium. Specific examples are studied.

On Spectral-Homotopy Perturbation Method Solution of Nonlinear Differential Equations in Bounded Domains

2013 ◽  
Vol 1 (1) ◽  
pp. 25-37
Author(s):  
Ahmed A. Khidir
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Boundary ◽  
Nonlinear Differential Equations ◽  
Iteration Algorithm ◽  
Test Problems ◽  
Nonlinear Boundary Value Problems ◽  
Homotopy Perturbation ◽  
Spectral Technique ◽  
Homotopy Analysis

In this study, a combination of the hybrid Chebyshev spectral technique and the homotopy perturbation method is used to construct an iteration algorithm for solving nonlinear boundary value problems. Test problems are solved in order to demonstrate the efficiency, accuracy and reliability of the new technique and comparisons are made between the obtained results and exact solutions. The results demonstrate that the new spectral homotopy perturbation method is more efficient and converges faster than the standard homotopy analysis method. The methodology presented in the work is useful for solving the BVPs consisting of more than one differential equation in bounded domains. 

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