A symptotic solution of the problem of the cylindrical bending of a plate of finite breadth in an elastic half-space

1974 ◽  
Vol 10 (7) ◽  
pp. 749-754 ◽  
Author(s):  
V. M. Aleksandrov ◽  
M. D. Solodovnik
Keyword(s):  
Half Space ◽  
Elastic Half Space ◽  
Cylindrical Bending ◽  
Finite Breadth

The efficiency of application of virtual cross-sections method and hypotheses MELS in problems of wave signal propagation in elastic waveguides with rough surfaces

2016 ◽  
pp. 3564-3575 ◽  
Author(s):  
Ara Sergey Avetisyan
Keyword(s):  
Half Space ◽  
Cross Sections ◽  
Classical Method ◽  
Signal Propagation ◽  
Elastic Half Space ◽  
Layered Systems ◽  
Surface Layers ◽  
Inhomogeneous Surface ◽  
Wave Signal ◽  
The Impact

The efficiency of virtual cross sections method and MELS (Magneto Elastic Layered Systems) hypotheses application is shown on model problem about distribution of wave field in thin surface layers of waveguide when plane wave signal is propagating in it. The impact of surface non-smoothness on characteristics of propagation of high-frequency horizontally polarized wave signal in isotropic elastic half-space is studied. It is shown that the non-smoothness leads to strong distortion of the wave signal over the waveguide thickness and along wave signal propagation direction as well.  Numerical comparative analysis of change in amplitude and phase characteristics of obtained wave fields against roughness of weakly inhomogeneous surface of homogeneous elastic half-space surface is done by classical method and by proposed approach for different kind of non-smoothness.

Guided Surface Waves on an Elastic Half Space

1971 ◽  
Vol 38 (4) ◽  
pp. 899-905 ◽  
Author(s):  
L. B. Freund
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Surface Waves ◽  
Half Space ◽  
Body Wave ◽  
Three Dimensional ◽  
Elastic Half Space ◽  
Normal Displacement ◽  
Rigid Barrier ◽  
Wave Disturbances

Three-dimensional wave propagation in an elastic half space is considered. The half space is traction free on half its boundary, while the remaining part of the boundary is free of shear traction and is constrained against normal displacement by a smooth, rigid barrier. A time-harmonic surface wave, traveling on the traction free part of the surface, is obliquely incident on the edge of the barrier. The amplitude and the phase of the resulting reflected surface wave are determined by means of Laplace transform methods and the Wiener-Hopf technique. Wave propagation in an elastic half space in contact with two rigid, smooth barriers is then considered. The barriers are arranged so that a strip on the surface of uniform width is traction free, which forms a wave guide for surface waves. Results of the surface wave reflection problem are then used to geometrically construct dispersion relations for the propagation of unattenuated guided surface waves in the guiding structure. The rate of decay of body wave disturbances, localized near the edges of the guide, is discussed.

scholarly journals Group and Phase Velocity of Love Waves Propagating in Elastic Functionally Graded Materials

2015 ◽  
Vol 40 (2) ◽  
pp. 273-281 ◽  
Author(s):  
Piotr Kiełczyński ◽  
Marek Szalewski ◽  
Andrzej Balcerzak ◽  
Krzysztof Wieja
Keyword(s):  
Group Velocity ◽  
Half Space ◽  
Functionally Graded Materials ◽  
Integral Formula ◽  
Liouville Problem ◽  
Elastic Half Space ◽  
Functionally Graded ◽  
Love Waves ◽  
Graded Materials ◽  
Sturm Liouville

AbstractThis paper presents a theoretical study of the propagation behaviour of surface Love waves in nonhomogeneous functionally graded elastic materials, which is a vital problem in acoustics. The elastic properties (shear modulus) of a semi-infinite elastic half-space vary monotonically with the depth (distance from the surface of the material). Two Love wave waveguide structures are analyzed: 1) a nonhomogeneous elastic surface layer deposited on a homogeneous elastic substrate, and 2) a semi-infinite nonhomogeneous elastic half-space. The Direct Sturm-Liouville Problem that describes the propagation of Love waves in nonhomogeneous elastic functionally graded materials is formulated and solved 1) analytically in the case of the step profile, exponential profile and 1cosh2type profile, and 2) numerically in the case of the power type profiles (i.e. linear and quadratic), by using two numerical methods: i.e. a) Finite Difference Method, and b) Haskell-Thompson Transfer Matrix Method.The dispersion curves of phase and group velocity of surface Love waves in inhomogeneous elastic graded materials are evaluated. The integral formula for the group velocity of Love waves in nonhomogeneous elastic graded materials has been established. The results obtained in this paper can give a deeper insight into the nature of Love waves propagation in elastic nonhomogeneous functionally graded materials.

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