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The dynamics of structures on an elastic base

Abstract

The problem of the dynamics of structures interacting with an elastic homogeneous half-plane through a rigid unyielding plate is reduced to the construction of the matrix of transmission momentum functions (the Green's matrix), which establishes the dependence between the generalized coordinates of the oscillations of the plate and the force characteristics. The elements obtained for this matrix are represented by graphs as the result of numerical solution of the nonsteady-state dynamic contact problem. We conclude that approximating a Green's matrix of exponential type on an infinite time interval is unjustified.

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Literature cited

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    L. I. Slepyan,The Mechanics of Cracks [in Russian], Sudostroeniya, Leningrad (1981).

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    V. A. Karpenko and V. V. Cheporov, “Nonsteady-state shift oscillations of a plate for an inhomogeneous base,”Dinam. Sist, No. 4, (1985), 52–57.

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    V. A. Il'ichev, “Dynamic interaction of structures with a base and transmission of vibrations through a ground (industrial seismics),” in:Dynamical Calculation of Structures under Special Actions [in Russian], Stroiizdat, Moscow (1981), pp. 114–128.

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Additional information

Translated fromDinamicheskie Sistemy, No. 6, 1987, pp. 60–63.

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Tishchenko, V.N., Cheporov, V.V. The dynamics of structures on an elastic base. J Math Sci 57, 3400–3402 (1991). https://doi.org/10.1007/BF01097711

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Keywords

  • Contact Problem
  • Exponential Type
  • Dynamic Contact
  • Infinite Time
  • Momentum Function