Rayleigh’s approximation method on reflection/refraction phenomena of plane SH-wave in a corrugated anisotropic structure

2018 ◽  
pp. 297-326
Author(s):  
Neelima Bhengra
Keyword(s):  
Approximation Method ◽  
Anisotropic Structure ◽  
Sh Wave ◽  
Plane Sh Wave

Scattering of Anti-Plane SH-Wave by the Semi-Cylindrical Gap with Multiple Shallow-Buried Inclusions in Elastic Semi-Space

2012 ◽  
Vol 569 ◽  
pp. 78-81
Author(s):  
Hong Liang Li ◽  
Jing Guo ◽  
Li Ming Cai
Keyword(s):  
Displacement Field ◽  
Ground Surface ◽  
Analytic Solutions ◽  
Polar Coordinate System ◽  
Algebraic Equations ◽  
Sh Wave ◽  
Dynamic Stress Concentration Factor ◽  
Polar Coordinate ◽  
Cylindrical Inclusions ◽  
Plane Sh Wave

Semi-cylindrical gap and Multiple circular inclusions exists widely in natural media, composite materials and modern municipal construction. The scattering field produced by semi-cylindrical gap and multiple circular inclusions determines the dynamic stress concentration factor around the gap and circular inclusions, and therefore determines whether the material is damaged or not. These problems are complicated. It is hard to obtain analytic solutions except for several simple conditions. In this paper, the solution of displacement field for elastic semi-space with semi-cylindrical gap and multiple cylindrical inclusions by anti-plane SH-wave is constructed. In complex plane, considering the symmetry of SH-wave scattering , the displacement field aroused by the anti-plane SH-wave and the scattering displacement field impacted by the gap and the cylindrical inclusions comprised of Fourier-Bessel series with undetermined coefficients which satisfies the stress-free condition on the ground surface are constructed. Through applying the method of multi-polar coordinate system, the equations with unknown coefficients can be obtained by using the displacement and stress condition around the edge of the gap and cylindrical inclusions. According to orthogonality condition for trigonometric function, these equations can be reduced to a series of algebraic equations. Then the value of the unknown coefficients can be obtained by solving these algebraic equations. The total wave displacement field is the superposition of the displacement field aroused by the anti-plane SH-wave and the scattering displacement field. By using the expressions, an example is provided to show the effect of the change of relative location of the cylindrical inclusions.

Band Gaps of SH Wave in Piezoelectric Phononic Crystal

2011 ◽  
Vol 239-242 ◽  
pp. 1486-1489
Author(s):  
Man Lan ◽  
Pei Jun Wei
Keyword(s):  
Dispersion Equation ◽  
Elastic Waves ◽  
Phononic Crystal ◽  
Stop Band ◽  
Slope Angle ◽  
Band Gaps ◽  
Pass Band ◽  
Wave Band ◽  
Sh Wave ◽  
Plane Sh Wave

The dispersive characteristic of anti-plane elastic waves propagating through laminated piezoelectric phononic crystal is studied in this paper. First, the transfer matrix method (TMM) and the Bloch theorem are used to derive the dispersion equation. Next, the dispersion equation is solved numerically and the dispersive curves are shown in Brillouin zone. The pass band and the stop band of anti-plane SH wave propagating perpendicular to and oblique to the laminated periodic structure are compared. The effects of the slope angle on the wave band structure are discussed.

Incident Wave and Dislocation Acceleration Effects in Dislocation Emission From Cracks

1990 ◽  
Vol 57 (4) ◽  
pp. 870-876 ◽  
Author(s):  
L. M. Brock ◽  
J.-S. Wu
Keyword(s):  
Exact Solution ◽  
Yield Stress ◽  
Stress Level ◽  
Equation Of Motion ◽  
Dislocation Emission ◽  
Sinusoidal Wave ◽  
Sh Wave ◽  
Wave Parameters ◽  
Subcritical Speed ◽  
Plane Sh Wave

Some previous transient analyses of dislocation emission from dynamically loaded cracks have treated glide at constant speeds, and have invoked an emissions criterion that allows the dislocation force to exceed the yield stress level during glide. In the context of nonstrain-hardening plasticity, this analysis requires that the force remain at the yield stress level. For an exact solution to the problem of screw dislocation emission from a crack subjected to plane SH-wave diffraction, the result is an equation of motion for the dislocation, which can be integrated exactly. The dislocation is found to accelerate during glide to a high but subcritical speed, before decelerating to its arrest position. A general incident SH-wave is considered, but is then specialized to the cases of a step-stress and a sinusoidal wave. Calculations on the basis of material and wave parameters show that purely brittle fracture can be difficult to achieve, and that wavelength/frequency cutoffs exist, beyond which emission cannot occur.

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