Analysis of Vibration Insulation Properties of a Plate in an Elastic Medium Under the Influence of Different Types of Waves

  • N. A. LoktevaEmail author
  • D. V. Tarlakovskii
Conference paper
Part of the Structural Integrity book series (STIN, volume 8)


The vibration-absorbing properties of the plate under the action of the flat, cylindrical and spherical harmonic wave in the soil are studied. In the soil model, an elastic isotropic medium is used. The motion of the plate is described by the system of equations of Paimushin V.N. The mathematical formulation of the problem includes the assignment of the incident wave, the equations of motion of the soil and the plates, the boundary conditions for the slab and the soil, the conditions at infinity, and the conditions of contact of the earth with the obstacle, where we neglect the connection of the plate to the ground. The kinematic parameters of the plate and the parameters of the disturbed stress-strain state of the soil 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. The main goal is to determine the total vector field of acceleration for each type of waves.


Soil Plate V.T. paymushin model Flat wave Cylindrical wave Spherical harmonic wave Frequency Vibrations Vibration absorption Vibration acceleration 


  1. 1.
    Umek A.: Dynamic responses of building foundations to incident elastic waves. Ph.D. Thesis. Illinois, Ill. Inst. Technol (1973)Google Scholar
  2. 2.
    Kostrov, B.V.: Motion of a rigid massive wedge inserted into an elastic medium under the effect of plane wave. Prikl. Mat. Mekh. 28(1), 99–110 (1964). (In Russian)MathSciNetGoogle Scholar
  3. 3.
    Rylko, M.A.: On the motion of a rigid rectangular insertion under the effect of plane wave. Mekh. Tverd. Tela. 1, 158–164 (1977). (In Russian)Google Scholar
  4. 4.
    Rakhmatulin, K.A., Sunchalieva, L.M.: Elastic and elastoplastic properties of the ground upon dynamic loads on the foundation. Department in VINITI, pp. 4149–83 (1983) (In Russian)Google Scholar
  5. 5.
    Berezhnoi, D.V., Konoplev, Y.G., Paimushin V.N., Sekaeva, L.R.: Investigation of the interaction between concrete collector and dry and waterlogged grounds. Trudy Vseros. nauch. konf. “Matematicheskoe modelirovanie i kraevye zadachi” [Proc. All-Russ. Sci. Conf. “Mathematical Simulation and Boundary Value Problems”]. Part 1. Mathematical Models of Mechanics, Strength and Reliability of Structures. Samara, SamGTU, pp. 37–39 (2004) (In Russian)Google Scholar
  6. 6.
    Gorshkov, A.G., Medvedskii, A.L., Rabinskii, L.N., Tarlakovskii, D.V.: Waves in Continuum Media, p. 472. Fizmatlit, Moscow (2004). (In Russian)Google Scholar
  7. 7.
    Ivanov, V.A., Paimushin, V.N.: Refined formulation of dynamic problems of three-layered shells with a transversally soft filler is a numerical-analytical method for solving them. Appl. Mech. Tech. Phys. 36(4), 147–151 (1995)CrossRefGoogle Scholar
  8. 8.
    Ivanov, V.A., Paimushin, V.N.: Refinement of the equations of the dynamics of multilayer shells with a transversally soft filler. Izv. RAS. MTT 3, 142–152 (1995)Google Scholar
  9. 9.
    Sheddon, I.: Fourier Transforms, p. 542. McGraw Hill, New York (1951)Google Scholar

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Authors and Affiliations

  1. 1.Moscow Aviation Institute (National Research University)MoscowRussia
  2. 2.Institute of Mechanics Lomonosov Moscow State UniversityMoscowRussia

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