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Interaction of a Spherical Wave with a Rectangular Plate in a Ground

  • Natalya A. LoktevaEmail author
  • Dmitrii V. Tarlakovskii
Chapter
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 110)

Abstract

The vibration-absorbing properties of the plate under the action of a spherical harmonic wave propagating in the ground are studied. An elastic isotropic medium is used as a ground model. The main aim of this study is to determine the total vector field of accelerations. The mathematical formulation of the problem includes the assignment of the ingoing wave, the dynamic equations of the ground and the plate, the boundary conditions for the obstacle and the medium, the conditions at infinity for medium, and the conditions of contact of the medium with the obstacle, where we neglect the connection of the plate to the ground. The dynamic equations of the plate is described by the system of equations of V.N. Paimushin. The kinematic parameters of the plate and the parameters of the disturbed stress-strain state of the medium are represented in the form of double trigonometric series satisfying the boundary conditions. After that, the constants of integration, displacement, and vibration acceleration are determined.

Notes

Acknowledgements

The reported study was funded by Russian Foundation for Basic Research, according to the research projects Nos. 19-08-00968 A.

References

  1. 1.
    Gorshkov, A.G., Medvedskii, A.L., Rabinskii, L.N., Tarlakovskii, D.V.: Waves in Continuum Media. FIZMATLIT, Moscow (2004)Google Scholar
  2. 2.
    Ivanov, V., Paimushin, V.: Refined formulation of dynamic problems of three-layer shells with a transversally soft filler numerical-analytical method for solving them. Appl. Mech. Eng. Phys. 36(4), 147–151 (1995a)Google Scholar
  3. 3.
    Ivanov, V., Paimushin, V.: Rrefinement of the equations of the dynamics of multi-layer shells with transversally soft filler. Sol. Mech. 3, 142–152 (1995b)Google Scholar
  4. 4.
    Kostrov, B.V.: Motion of the rigid massive strip immersed in the elastic medium under the action of the plane wave. Appl. Math. Mech. 28(1) (1964)Google Scholar
  5. 5.
    Müller, G., Heckl, M.H.: Taschenbuch der Technischen Akustik. Heildelberg, New York, Berlin (2004)Google Scholar
  6. 6.
    Rakhmatulin, K.A.: Elastic and elastoplastic properties of the ground upon dynamic loads on the foundation. Dep in VINITI 4149–4183 (1983)Google Scholar
  7. 7.
    Rylko, M.: On movement of rigid rectangular inclusions in elastic medium affected by flat wave. Mech. Solids (1) (1977)Google Scholar
  8. 8.
    Sheddon, I.: Fourier Transforms. McGraw Hill, New York (1951)Google Scholar
  9. 9.
    SR: Set of Regulations on Design and Construction. SR no. 23-105-2004. Assessing Vibration during Design and Construction and Exploitation of Underground Objects. Moscow (2004)Google Scholar
  10. 10.
    Umek, A.: Dynamic responses of building foundations to incident elastic waves. Ph.D. Thesis, Illinois Institute of Technology, Illinois (1973)Google Scholar
  11. 11.
    Vyalov, S.S.: Problems in the theory of deformability of cohesive soils. Osn Fundam Mekh Gruntov 3, 1–4 (1966)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Moscow Aviation Institute National Research UniversityMoscowRussian Federation
  2. 2.Lomonosov Moscow State University, MoscowMoscowRussian Federation

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