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Reflection, transmission and excitation of SH-surface waves by a discontinuity in mass-loading on a semi-infinite elastic medium

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Abstract

The scattering of an SH-wave by a discontinuity in mass-loading on a semi-infinite elastic medium is investigated theoretically. The incident wave is either a plane body wave or a plane SH-surface wave. The problem is reduced to a Wiener-Hopf problem for the scattered wave. In this problem the amplitude spectral density of the particle displacement occurs as unknown function. Special attention is given to the numerical values of the surface wave contributions to the scattered field.

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Abbreviations

x 1, x 2, x 3 :

Cartesian coordinates

γ, χ :

polar coordinates in x 1, x 3-plane

ρ :

volume mass density

σ :

surface mass density of mass-loading

λ, μ :

Lamé constants

U :

scalar wave function, defined by (2.1)

c S :

speed of propagation of uniform shear waves in bulk medium (c S=(μ/ρ)1/2)

ω :

angular frequency

t :

time

k S :

wave number of uniform shear waves (k S=ω/c S)

η :

reduced specific acoustic impedance of mass-loading (η=k S σ/ρ)

k m :

wave number of SH-surface wave (k m=k S(1+η 2)1/2)

∂ 1,2,3 :

partial differentiation with respect to x 1,2,3

θ i :

angle between x 3-axis and direction of propagation of incident body wave

α i :

wave number in horizontal direction of incident body wave (α i=k S sin(θ i))

γ i :

wave number in vertical direction of incident body wave (γ i=k S cos(θ i))

C 1,2 :

complex amplitude of surface wave excited by a body wave

R :

reflection factor of surface wave, when surface wave is incident

T :

transmission factor of surface wave, when surface wave is incident

S :

particle displacement vector

References

  1. White, R. M., Proc. IEEE 58 (1970) 1238.

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  2. Noble, B., Methods based on the Wiener-Hopf technique for the solution of partial differential equations, Pergamon Press, London, New York, Paris, Los Angeles, 1958.

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  3. Alsop, L. E., A. S. Goodman, and E. Ash, The J. of the Acoustical Soc. of America, 50 (1971) 179.

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  4. Kay, A. F., IRE Trans. AP-7 (1959) 22.

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  5. Quak, D., Reflection, transmission and excitation of SH-surface waves by a discontinuity in mass-loading on a semi-infinite elastic medium, Report number 1973-7, Dept. of Elect. Eng., Div. of Electromagnetic Res. Delft Univ. of Technology, Delft, The Netherlands (In Dutch).

  6. Tournois, P. and C. Lardat, IEEE Trans. SU-16 (1969) 107.

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Authors and Affiliations

  1. Dept. of Elect. Eng., Div. of Electromagnetic Res., Delft Univ. of Technology, Delft, The Netherlands

    D. Quak & F. L. Neerhoff

Authors
  1. D. Quak
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  2. F. L. Neerhoff
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Additional information

The research presented in this paper has been carried out with partial financial support from the Delfts Hogeschoolfonds.

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Quak, D., Neerhoff, F.L. Reflection, transmission and excitation of SH-surface waves by a discontinuity in mass-loading on a semi-infinite elastic medium. Appl. Sci. Res. 29, 447–460 (1974). https://doi.org/10.1007/BF00384165

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  • DOI: https://doi.org/10.1007/BF00384165

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