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

doi:10.1016/0165-2125(86)90016-8

Wave Motion

Volume 8, Issue 4, July 1986, Pages 371-379

https://doi.org/10.1016/0165-2125(86)90016-8 Get rights and content

Abstract

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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^∗: Now at Department of Mechanics, Huazhong University of Science and Technology, Wuhan, Hubei, China.

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

Abstract

Multiple scattering of elastic waves by cylinders of arbitrary cross section. I. SH Waves

J. Acoust. Soc. Amer.

A propagator model for scattering of acoustic waves by bubbles in water

J. Acoust. Soc. Amer.

Wave propagation in randomly cracked media

Partial differential equations with periodic coefficients and Bloch waves in crystals

J. Math. Phys.