International Applied Mechanics

, Volume 51, Issue 3, pp 303–310 | Cite as

Nonstationary Load on the Surface of an Elastic Half-Strip


A method for determining the stress-strain state of an elastic half-strip under a nonstationary load applied to its boundary is proposed. The corresponding initial-boundary-value problem is formulated. The Laplace transform is used and the solution is expanded into a Fourier series. The variation in the stress and displacement with time and space coordinates is studied


elasticity plane problem nonstationary processes stress state Laplace transform 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    H. Bateman and A. Erdelyi, Tables of Integral Transforms, Vol. 1, McGraw-Hill, New York (1954).Google Scholar
  2. 2.
    H. Bateman and A. Erdelyi, Higher Transcendental Functions, McGraw-Hill, New York (1953).Google Scholar
  3. 3.
    A. G. Gorshkov and D. V. Tarlakovskii, Dynamic Contact Problems with Moving Boundaries [in Russian], Fizmatgiz, Moscow (1995).Google Scholar
  4. 4.
    A. N. Guz, V. D. Kubenko, and M. A. Cherevko, Diffraction of Elastic Waves [in Russian], Naukova Dumka, Kyiv (1978).Google Scholar
  5. 5.
    V. D. Kubenko, “Stress state of an elastic half-plane under nonstationary loading,” Int. Appl. Mech., 51, No. 2, 121–129 (2015).MathSciNetCrossRefADSGoogle Scholar
  6. 6.
    V. B. Poruchikov, Methods of Dynamic Elasticity [in Russian], Nauka, Moscow (1986).Google Scholar
  7. 7.
    I. I. Anik’ev, V. A. Maksimyuk, M. I. Mikhailova, and E. A. Sushchenko, “Incidence of a shock wave on a cantilever plate coupled with an elastic rod,” Int. Appl. Mech., 49, No. 4, 482–487 (2013).CrossRefADSGoogle Scholar
  8. 8.
    I. I. Anik’ev, V. A. Maksimyuk, M. I. Mikhailova, and E. A. Sushchenko, “Nonstationary behavior of a cantilever–rod system under nearly critical loads,” Int. Appl. Mech., 49, No. 5, 570–575 (2013).CrossRefADSGoogle Scholar
  9. 9.
    I. I. Anik’ev, M. I. Mikhailova, and E. A. Sushchenko, “Influence of a patch on the deformation of an elastic plate with an edge notch under the action of a shock wave,” Int. Appl. Mech., 50, No. 4, 470–475 (2014).MATHCrossRefADSGoogle Scholar
  10. 10.
    M. C. M. Bakker, B. J. Kooij, and M. D. Verweij, “A knife-edge load traveling on the surface of an elastic halfspace,” Wave Motion, 49, 165–180 (2012).CrossRefGoogle Scholar
  11. 11.
    L. Cagniard, Reflexion et Refractiondes Ondes Seismiques, Paris (1939).Google Scholar
  12. 12.
    L. In-Mo, “Transient groundmotion in an elastic homogeneous halfspace to blasting loading,” Soil Dynam. Earthquake Eng., 15, No. 3, 151–159 (1996).CrossRefGoogle Scholar
  13. 13.
    V. D. Kubenko, “Nonstationary contact of a rigid body with an elastic medium: Plane problem,” Int. Appl. Mech., 48, No. 5, 487–551 (2012).MATHCrossRefADSGoogle Scholar
  14. 14.
    E. Mesquita, H. Antes, L. H. Thomazo, and M. Adolph, “Transient wave propagation phenomena at visco-elastic half-spaces under distributed surface loadings,” Lat. Am. J. Solids Struct., 9, No. 4 (2012).Google Scholar
  15. 15.
    R. G. Payton, “Transient motion of an elastic half-space due to a moving surface line load,” Int. J. Eng. Sci., 5, No. 1, 40–79 (1967).MATHCrossRefGoogle Scholar
  16. 16.
    A. R. Robinson and J. C. Thompson, “Transient stresses in an elastic half space resulting from the frictionless indentation of a rigid wedge-shaped die,” ZAMM, 54, No. 3, 139–144 (1974).MATHCrossRefGoogle Scholar
  17. 17.
    X. Zhao, S. A. Meguid, and K. M. Liew, “The transient response of bonded piezoelectric and elastic half space with multiple interfacial collinear cracks,” Acta Mech., 159, 11–27 (2002).MATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.S. P. Timoshenko Institute of MechanicsNational Academy of Sciences of UkraineKyivUkraine

Personalised recommendations