Acta Mechanica Solida Sinica

, Volume 20, Issue 3, pp 258–265 | Cite as

Exact solution for a two-dimensional Lamb’s problem due to a strip impulse loading

  • Guangyu Liu
  • Kaixin Liu


By applying the integral transform method and the inverse transformation technique based upon the two types of integration, the present paper has successfully obtained an exact algebraic solution for a two-dimensional Lamb’s problem due to a strip impulse loading for the first time. With the algebraic result, the excitation and propagation processes of stress waves, including the longitudinal wave, the transverse wave, and Rayleigh-wave, are discussed in detail. A few new conclusions have been drawn from currently available integral results or computational results.

Key words

Lamb’s problem exact solution integral transform strip impulse loading excitation and propagation of elastic waves 


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  1. [1]
    Lamb, H., On the propagation of tremors over the surface of an elastic solid. Philosophical Transactions of the Royal Society (London), 1904, 203, A: 1–42.CrossRefGoogle Scholar
  2. [2]
    Cagniard, L., Reflexion et Refraction des Ondes Seismiques Progressives. Cauthiers- Villars, Paris, 1939; translated into English and revised by Flinn, E.A. and Dix, C.H. Reflection and Refraction of Progressive Seismic Waves. New York: McGraw-Hill, 1962.zbMATHGoogle Scholar
  3. [3]
    De Hoop, A.T., A modification of Cagniard’s method for solving seismic pulse problem. Appl Sci Res, 1960, B8: 349–356.CrossRefGoogle Scholar
  4. [4]
    Pekeris, C.L., The seismic buried pulse//Proc Nat Acad Sci, 1955, 41: 629–639.MathSciNetCrossRefGoogle Scholar
  5. [5]
    Chao, C.C., Dynamical response of an elastic half-space to tangential surface loading. ASME J Appl Mech, 1960, 27: 559–567.MathSciNetCrossRefGoogle Scholar
  6. [6]
    Johnson, L.R., Green’s function for Lamb’s problem. Geophysics J R Astr Soc, 1974, 37: 99–131.CrossRefGoogle Scholar
  7. [7]
    Dix, C.H., The method of Cagniard in seismic pulse problems. Geophysics, 1954, 19: 722–738.CrossRefGoogle Scholar
  8. [8]
    Pinney. E., Surface motion due to a point source in a semi-infinite elastic medium. Bull Seism Soc Am, 1954, 44: 571–596.MathSciNetGoogle Scholar
  9. [9]
    Pekeris, C.L., The seismic surface pulse//Proc Nat Acad Sci, 1955, 41: 469–480.MathSciNetCrossRefGoogle Scholar
  10. [10]
    Pekeris, C.L., Lifson H. Motion of the surface of a uniform elastic half space produced by a buried pulse. J Acoust Soc Am, 1957, 29: 1233–1238.MathSciNetCrossRefGoogle Scholar
  11. [11]
    Aggarwal, H.R. and Ablow, C.M., Solution to a class of three-dimensional pulse propagation in an elastic half-space. Int J Engng Sci, 1967, 5: 663–679.CrossRefGoogle Scholar
  12. [12]
    Wang, K.C. and Wang, Y.S., Surface displacement of an elastic half-space due to a vertically buried point-source load. Acta Mechanica Solida Sinica, 1983, 4(3): 427–434 (in Chinese).MathSciNetGoogle Scholar
  13. [13]
    Zheng, J.L., Fundamental solutions of elastic half-space for dynamic problems. Acta Mechanica Solida Sinica, 1988, 9(1): 76–81 (in Chinese).Google Scholar
  14. [14]
    Mooney, H.M., Some numerical solutions for Lamb’s problem. Bull. Seismological Soc. Amer., 1974, 64(2): 473–491.Google Scholar
  15. [15]
    Takemiya, H., Member, ASCE and Guan, F., Transient Lamb’s solution for surface strip impulses. Journal of Engineering Mechanics, 1993, 119: 2385–2403.CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2007

Authors and Affiliations

  • Guangyu Liu
    • 1
  • Kaixin Liu
    • 1
  1. 1.LTCS and Department of Mechanics & Aerospace Engineering, College of EngineeringPeking UniversityBeijingChina

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