Plane problem on beam plate’s oscillations on on rectangular base

Authors

  • N. Vaysfeld King's college, Strand building, S2.35, London
  • Yu. Protserov Odessa I. I. Mechnikov National University
  • A. Tolkachov Odessa I. I. Mechnikov National University

DOI:

https://doi.org/10.17721/1812-5409.2023/2.12

Keywords:

rectangular base, beam, dynamic contact stress

Abstract

The plane contact problem of a beam’s oscillations on a rectangular elastic base is considered. The vertical edges of the rectangular base are in conditions of the nonfriction contact, the lower edge is fixed, and a beam (beam plate) with free ends is attached to the upper edge. The normal loading is applied to the beam and harmonically changes in time. To solve the boundary valued problem for the elastic base the integral transform method is applied. The apparatus of the Green’s function is used to construct the solution for the boundary valued problem for a beam. The displacements of the rectangular base and the deflection of the beam were found. The interface condition between the base and the plate is used to derive the integral singular equation relatively the dynamical contact stress. The orthogonal polynomial method was used to solve the integral equation. The investigation of the oscillations’ frequency influence on the deflection of beam and elastic rectangular base’s displacements and stress was conducted.

Pages of the article in the issue: 96 - 99

Language of the article: Ukrainian

References

ULITKO, A. (2002) Vectorni rozkladennya u prostoroviy teorii prugnosti. Kyiv, Academperiodyka.

ОSTRIK, V., UlLITKO, A. (2006) Wiener-Hopf Method in Contact Problems of Elasticity. Kyiv, Naukova dumka.

POPOV, G., REUT, V., MOISEEV, N., VAYSFELD, N. (2010) Rivnyannya matematychoi fizyki. Odesa, Astroprint.

SEIMOV, V. (1976) Dynamic contact problems. Kyiv, Naukova dumka.

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Published

2023-12-23

How to Cite

Vaysfeld, N., Protserov, Y., & Tolkachov, A. (2023). Plane problem on beam plate’s oscillations on on rectangular base. Bulletin of Taras Shevchenko National University of Kyiv. Physical and Mathematical Sciences, (2), 96–99. https://doi.org/10.17721/1812-5409.2023/2.12

Issue

Section

Differential equations, mathematical physics and mechanics