Reflection and transmission of scalar waves by a periodic array of screens

Achenbach, Jan Drewes; Li, Z. L.

doi:10.1016/s0165-2125(86)80045-2

Cited by 79 publications

(38 citation statements)

References 7 publications

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“…In this case the continuity equation (1) becomes (3) Also, the momentum equation can be written as (4) where it was denoted The relationships (3) and (4) give the equation for the pressure (5) Here we have used the notation (6) Equation (4) and Equation (5) constitute a system of four Partial Differential Equations for determining the pressure and velocity fields.…”

Section: The Equations Of the Motion Of A Viscous Fluid In Linear Acomentioning

confidence: 99%

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Influence of viscosity on the reflection and transmission of an acoustic wave by a periodic array of screens: The general 3-D problem

Homentcovschi

Miles

2008

Wave Motion

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An analysis is presented of the diffraction of a pressure wave by a periodic grating including the influence of the air viscosity. The direction of the incoming pressure wave is arbitrary. As opposed to the classical nonviscous case, the problem cannot be reduced to a plane problem having a definite 3-D character. The system of partial differential equations used for solving the problem consists of the compressible Navier-Stokes equations associated with no-slip boundary conditions on solid surfaces. The problem is reduced to a system of two hypersingular integral equations for determining the velocity components in the slits' plane and a hypersingular integral equation for the normal component of velocity. These equations are solved by using Galerkin's method with some special trial functions. The results can be applied in designing protective screens for miniature microphones realized in MEMS technology. In this case, the physical dimensions of the device are on the order of the viscous boundary layer so that the viscosity cannot be neglected. The analysis indicates that the openings in the screen should be on the order of 10 microns in order to avoid excessive attenuation of the signal. This paper also provides the variation of the transmission coefficient with frequency in the acoustical domain.

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Section: The Equations Of the Motion Of A Viscous Fluid In Linear Acomentioning

confidence: 99%

“…Miles [2] studied the case of a grating of inclined .at plates in a one-mode approximation for small screens. Achenbach and Li [3] have developed an exact method suitable for arbitrary frequency and incidence. They utilized a periodic Green's function to reduce the problem to a singular integral equation.…”

Section: Introductionmentioning

confidence: 99%

Influence of viscosity on the reflection and transmission of an acoustic wave by a periodic array of screens: The general 3-D problem

Homentcovschi

Miles

2008

Wave Motion

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“…The incident field win satisfies equation (1). Therefore the scattered field w Sc must also satisfy the same equation.…”

Section: Statement Of the Problemmentioning

confidence: 99%

“…This study was motivated by the desire to better understand the detection and characterization of a flaw plane, i.e., a plane of microcracks, in a more realistic situation. The first thing we can do to model a flaw plane is to model it as a periodic array of cracks [1][2][3][4][5]. In reality, however, an array of cracks is never periodic but rather random.…”

Section: Introductionmentioning

confidence: 99%

Scattering by an Infinite Array of Randomly Spaced Coplanar Cracks

Mikata

1993

Review of Progress in Quantitative Nondestructive Evaluation

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“…Scattering of scalar waves by a periodic array of screen was treated in [3]. An integral equation was derived for the unknown jump of the scalar potential across the screen, and this equation was again solved by an expansion in Chebyshev polynomials of the unknown jump.…”

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confidence: 99%

Scattering by a Periodic Array of Collinear Cracks

Mikata

Achenbach

1989

Review of Progress in Quantitative Nondestructive Evaluation

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This paper deals with the problem tlf scattering of an in-plane wave by a periodic array of collinear cracks in an elastic solid. The work is of interest for the detection of cracked zone in both quantitative evaluation of materials and seismology.Scattering by elastic waves, both normally incident anti-plane longitudinal waves, by a Griffith crack was studied by Mal [1]. An integral transform method was used In (1]. Van der Hijden and Neerhoff [2] also investigated the problem of scattering of in-plane longitudinal and transverse waves by a Griffith crack, and derived a set of integral equations for the unknown crack-opening displacements. The Chebyshev polynomial expansions of the unknown crack-opening displacements were used to solve these integral equations.In recent years, scattering of waves by a periodic structure has been intensively studied for the application in the quantitative nondestructive evaluation of materials. Scattering of scalar waves by a periodic array of screen was treated in [3]. An integral equation was derived for the unknown jump of the scalar potential across the screen, and this equation was again solved by an expansion in Chebyshev polynomials of the unknown jump. The boundary integral equation method has been used to solve the threedimensional problem of reflection and transmission of a longitudinal wave by a doubly periodic array of spherical cavities [4]. The same method has been also used to solve the problem of scattering by a periodic array of inclined cracks [5], where the scattering by a periodic array of collinear cracks has been treated as a special case. The problem of scattering of waves by a periodic array of collinear cracks was first treated by Angel and Achenbach (6,7], where it was solved by using Fourier series expansion of the GreenLame potentials. In this paper, we will solve the same problem by extending van der Hijden and Neerhoff's treatment [2] of in-plane wave scattering by a sigle crack. The merit of our treatment over Angel and Achenbach [6, 7) will be discussed.

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Reflection and transmission of scalar waves by a periodic array of screens

Cited by 79 publications

References 7 publications

Influence of viscosity on the reflection and transmission of an acoustic wave by a periodic array of screens: The general 3-D problem

Influence of viscosity on the reflection and transmission of an acoustic wave by a periodic array of screens: The general 3-D problem

Scattering by an Infinite Array of Randomly Spaced Coplanar Cracks

Scattering by a Periodic Array of Collinear Cracks

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