Reflection and Transmission by a Periodic Array of Coplanar Cracks: Normal and Oblique Incidence

1993 ◽  
Vol 60 (4) ◽  
pp. 911-919 ◽  
Author(s):  
Yozo Mikata
Keyword(s):  
Elastic Waves ◽  
Oblique Incidence ◽  
Numerical Results ◽  
Periodic Array ◽  
Fourier Series Expansion ◽  
Periodic Case ◽  
Single Crack ◽  
Reflection And Transmission ◽  
Numerical Integrations ◽  
Coplanar Cracks

Scattering of in-plane elastic waves by a periodic array of coplanar cracks is investigated. This problem was first treated by Angel and Achenbach. The method of their solution was based on the Fourier series expansion of the Green-Lame potentials. In this paper, we have extended van der Hijden and Neerhoff’s treatment of scattering of in-plane elastic waves by a single crack to the periodic case. Major advantages of our treatment over Angel and Achenbach are: (1) the formulation is relatively simple, straightforward, and unified for both normal and oblique incidence, and (2) more importantly, there is no need for numerical integrations, because all the integrations involved in the formulation can be analytically evaluated thanks to the periodicity of the problem and the coplanarity of the cracks. Numerical results are presented and compared with those of Angel and Achenbach. Some new numerical results are also presented.

SH-Waves in a Medium Containing a Disordered Periodic Array of Cracks

1995 ◽  
Vol 62 (2) ◽  
pp. 312-319 ◽  
Author(s):  
Y. Mikata
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Numerical Results ◽  
Crack Spacing ◽  
Periodic Array ◽  
Wave Number ◽  
Sh Wave ◽  
Reflection And Transmission ◽  
Dispersion And Attenuation

Reflection and transmission of an SH-wave by a disordered periodic array of coplanar cracks is investigated, and subsequently its application to the dispersion and attenuation of an SH-wave in a disorderedly cracked medium is also treated. This is a stochastic boundary value problem. The formulation largely follows Mikata and Achenbach (1988b). The problem is formulated for an averaged scattered field, and the governing singular integral equation is derived for a conditionally averaged crack-opening displacement using a quasi-crystalline-like approximation. Unlike our previous study (Mikata and Achenbach, 1988b) where a point scatterer approximation was used for the regular part of the integral kernel, however, no further approximation is introduced. The singular integral equation is solved by an eigenfunction expansion involving Chebyschev polynomials. Numerical results are presented for the averaged reflection and transmission coefficients of zeroth order as a function of the wave number for normal incidence, a completely disordered crack spacing, and various values of the ratio of crack length and average crack spacing. Numerical results are also presented for the dispersion and attenuation of an SH-wave in a disorderedly cracked medium.

On the oblique incidence of elastic waves on a periodic array of obstacles

Wave Motion ◽  
2006 ◽  
Vol 43 (3) ◽  
pp. 193-205 ◽  
Author(s):  
Edoardo Scarpetta ◽  
Vincenzo Tibullo
Keyword(s):  
Elastic Waves ◽  
Oblique Incidence ◽  
Periodic Array

Reflection and transmission of elastic waves through nonlocal piezoelectric plates sandwiched in two solid half-spaces

2021 ◽  
Vol 168 ◽  
pp. 108306
Author(s):  
Cancan Liu ◽  
Jiangong Yu ◽  
Xianhui Wang ◽  
Bo Zhang ◽  
Xiaoming Zhang ◽  
...  
Keyword(s):  
Elastic Waves ◽  
Reflection And Transmission ◽  
Piezoelectric Plates

Reflection of plane elastic waves from transition layers with arbitrary varration of velocity and density

1966 ◽  
Vol 56 (3) ◽  
pp. 633-642 ◽  
Author(s):  
Ravindra N. Gupta
Keyword(s):  
Transition Layer ◽  
Elastic Waves ◽  
Numerical Results ◽  
Elastic Parameters ◽  
Transition Layers

abstract The problem of reflection of plane elastic waves is generalized numerically to an arbitrary variation, with depth, of the elastic parameters inside a transition layer between two homogeneous half-spaces. Numerical results are given for some cases of interest.

Reflection and transmission of elastic waves in a system of corrugated layers

1967 ◽  
Vol 57 (3) ◽  
pp. 393-419
Author(s):  
A. Levy ◽  
H. Deresiewicz
Keyword(s):  
Incident Wave ◽  
Elastic Waves ◽  
Scattered Field ◽  
Single Layer ◽  
Body Waves ◽  
Numerical Computations ◽  
Plane Body ◽  
Reflection And Transmission ◽  
Plane Parallel

abstract The scattered field generated by normally incident body waves in a system of layers having small, but otherwise arbitrary, periodic deviations from plane parallel boundaries is shown to consist of superposed plane body and surfacetype waves. Results of numerical computations for two like half-spaces separated by a sinusoidally corrugated single layer, and by two layers, reveal the variation of the amplitude of the field with ratios of velocities, densities, impedances, and with those of depth of layers and wavelength of the boundary corrugations to the wavelength of the incident wave.

Nonlinear Elastic Waves in a 1D Layered Composite Material: Some Numerical Results

2011 ◽  
Author(s):  
Igor Andrianov ◽  
Vladislav Danishevs’kyy ◽  
Dieter Weichert ◽  
Heiko Topol ◽  
Theodore E. Simos ◽  
...  
Keyword(s):  
Composite Material ◽  
Elastic Waves ◽  
Layered Composite ◽  
Numerical Results ◽  
Layered Composite Material ◽  
Nonlinear Elastic
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