TY - JOUR

T1 - Propagation of horizontally polarized transverse waves in a solid with a periodic distribution of cracks

AU - Achenbach, J. D.

AU - Li, Z. L.

N1 - Funding Information:
The work presentedh ere was carried out in the course of researchs ponsoredb y the Office of Naval Research( N00014-76-C-0063).

PY - 1986/7

Y1 - 1986/7

N2 - The propagation of time-harmonic waves in a solid containing a periodic distribution of cracks is investigated in a two-dimensional configuration. The cracks are parallel to the x-axis, and their centers are located at positions x = md, y = lh(m, l = 0, ±1, ±2,...). The wave motion is polarized in the z-direction and propagates in the y-direction (normal to the cracks). The theory of Floquet or Bloch waves, together with an appropriate Green's function and the condition of vanishing traction on the crack faces leads to a system of singular integral equations, which provides the basis for the derivation of an exact dispersion equation. Numerical results are presented for the wave number as a function of the frequency. The frequency spectrum shows a pattern of passing and stopping bands. The exact results are compared with the frequency spectrum according to a simplified theory which considers the arrays of collinear cracks in the planes y = lh (l= 0 ±1, ±2,...) as planes of homogeneous transmission and reflection. Good agreement is observed between exact and approximate results.

AB - The propagation of time-harmonic waves in a solid containing a periodic distribution of cracks is investigated in a two-dimensional configuration. The cracks are parallel to the x-axis, and their centers are located at positions x = md, y = lh(m, l = 0, ±1, ±2,...). The wave motion is polarized in the z-direction and propagates in the y-direction (normal to the cracks). The theory of Floquet or Bloch waves, together with an appropriate Green's function and the condition of vanishing traction on the crack faces leads to a system of singular integral equations, which provides the basis for the derivation of an exact dispersion equation. Numerical results are presented for the wave number as a function of the frequency. The frequency spectrum shows a pattern of passing and stopping bands. The exact results are compared with the frequency spectrum according to a simplified theory which considers the arrays of collinear cracks in the planes y = lh (l= 0 ±1, ±2,...) as planes of homogeneous transmission and reflection. Good agreement is observed between exact and approximate results.

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U2 - 10.1016/0165-2125(86)90016-8

DO - 10.1016/0165-2125(86)90016-8

M3 - Article

AN - SCOPUS:0022755384

VL - 8

SP - 371

EP - 379

JO - Wave Motion

JF - Wave Motion

SN - 0165-2125

IS - 4

ER -