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Applied Mathematics and Mechanics (English Edition) ›› 1999, Vol. 20 ›› Issue (11): 1222-1229.

• 论文 • 上一篇    下一篇

INVERSE PROBLEM FOR THE VISCOELASTIC MEDIUM WITH DISCONTINUOUS WAVE IMPEDANCE

陈显尧1, 程昌钧2,3   

  1. 1. Department of M echanics, Lanzhou University, Lanzhou 730000, P. R. China;
    2. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, P. R. China;
    3. Department of Mechanics, Shanghai University, Shanghai 200072, P. R. China
  • 收稿日期:1998-12-01 修回日期:1999-06-25 出版日期:1999-11-18 发布日期:1999-11-18
  • 基金资助:
    the National Natural Science Foundation of China(19772027)

INVERSE PROBLEM FOR THE VISCOELASTIC MEDIUM WITH DISCONTINUOUS WAVE IMPEDANCE

Chen Xianyao1, Cheng Changjun 2,3   

  1. 1. Department of M echanics, Lanzhou University, Lanzhou 730000, P. R. China;
    2. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, P. R. China;
    3. Department of Mechanics, Shanghai University, Shanghai 200072, P. R. China
  • Received:1998-12-01 Revised:1999-06-25 Online:1999-11-18 Published:1999-11-18
  • Supported by:
    the National Natural Science Foundation of China(19772027)

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摘要： In this paper, the inverse problem for the viscoelastic medium is investigated in the time domain, in which the wave impedance of the medium is discontinuous at the rear interface. The differentio-integral equations governing the behavior of the scattering and propagation operators are utilized to reconstruct the relaxation modulus of the viscoelastic medium. A new approach, in which only the one-side measurement reflection data for one round trip through the viscoelastic layer, is developed. The numerical examples are given at the end of the paper. It is shown that the curves of the reconstructed moduli coincide very well with the original relaxation moduli.

关键词: viscoelastic medium, inverse scattering, inversion procedure, Volterra integral equation, relaxation modulus, one round trip, numerical examples

Abstract: In this paper, the inverse problem for the viscoelastic medium is investigated in the time domain, in which the wave impedance of the medium is discontinuous at the rear interface. The differentio-integral equations governing the behavior of the scattering and propagation operators are utilized to reconstruct the relaxation modulus of the viscoelastic medium. A new approach, in which only the one-side measurement reflection data for one round trip through the viscoelastic layer, is developed. The numerical examples are given at the end of the paper. It is shown that the curves of the reconstructed moduli coincide very well with the original relaxation moduli.

Key words: viscoelastic medium, inverse scattering, inversion procedure, Volterra integral equation, relaxation modulus, one round trip, numerical examples

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