Steady-state harmonic oscillations of a layer weakened by two openings with end faces covered by diaphragm (a symmetric case)

Authors

  • Ю. Д. Ковалев Sumy State University, Sumy, Ukraine
  • Е. А. Стрельникова A. N. Podgorny Institute for Mechanical Engineering Problems, NAS of Ukraine, Kharkiv, Ukraine
  • Д. В. Кушнир Sumy State University, Sumy, Ukraine
  • Ю. В. Шрамко Sumy State University, Sumy, Ukraine

Keywords:

harmonic oscillations, layer with two opening, integral equations

Abstract

Steady-state harmonic oscillations of an elastic layer weakened by two through openings with pulsing normal pressure acting at their surfaces are under consideration. The integral representations of unknown functions based on the theory of homogeneous solutions with application of MacDonald special functions are in use. These representations allow us to satisfy automatically the boundary conditions on the surfaces of openings. The boundary problem is reduced to the system of six integral equations for every harmonics. Its solution is obtained numerically. Some numerical examples are presented. The isotropic layers with elliptical cylindrical surfaces are considered. The examples demonstrate some important characteristic features of the tension distribution and its influence on frequencies depending on the distance between openings and value of Poisson's ratio. The effect of widening the first resonance base via Poisson's ratio decreasing is observed. The influence of two openings on each other is investigated.

Author Biographies

Ю. Д. Ковалев, Sumy State University, Sumy

PhD

Е. А. Стрельникова, A. N. Podgorny Institute for Mechanical Engineering Problems, NAS of Ukraine, Kharkiv

Doctor of Technical Sciences

Д. В. Кушнир, Sumy State University, Sumy

PhD

Ю. В. Шрамко, Sumy State University, Sumy

PhD

References

Dawe D. J. Use of the finite strip method in predicting the behaviour of composite laminated structures / D. J. Dawe // Compos.Struct. - 2002. – Vol. 57. – P. 11-36.

Lure A. I. K teorii tolstyih plit / A. I. Lure // Prikl. matematika i mehanika. – 1942. – T. 6, vyip. 2/3. – S. 151 - 168.

Kosmodamianskiy A. S. Tolstyie mnogosvyaznyie plastinyi / A. S. Kosmodamianskiy, V. A. Shaldyirvan. – Kiev: Nauk. dumka, 1978. – 240 s.

Shaldyirvan V. A. O metode Lure-Vorovicha v smeshannyih zadachah izgiba tsilindricheskih tel / V. A. Shaldyirvan, T. A. Vasilev // Prikl. mehanika. – 2005. – T. 41, N 8. – S. 58 – 65.

Altuhov E. V. Uprugoe ravnovesie sloya s polostyu dlya granichnyih usloviy smeshannogo tipa na tortsah / E. V. Altuhov // Teoret. i prikl. mehanika. – 1993. – Vyip.24. – S. 3 - 7.

Kosmodamianskiy A. S. Kontsentratsiya napryazheniy pri izgibe tolstoy plityi s beskonechnyim ryadom polostey / A. S. Kosmodamianskiy, V. A. Shaldyirvan, G. G. Shaldyirvan // Prikl. mehanika. – 1975. – T.11, vyip. 4. – S. 15

Filshtinskiy L. A. Smeshannaya kososimmetrichnaya zadacha ob uprugom sloe, oslablennom skvoznyimi polostyami / L. A. Filshtinskiy, Yu. D. Kovalev // Fiziko-him. mehanika materialov. – 2001. – #5. – S. 114 - 116.

Filshtinskiy L. A. Garmonicheskoe vozbuzhdenie uprugogo sloya s polostyu / L. A. Filshtinskiy, Yu. D. Kovalyov, D. V. Kushnir // Materialyi XIV Mezhdunar. nauchnoy shk. im. akademika S. A. Hristianovicha. – Simferopol, 2004. – S. 151 - 153.

Bokov I. P. Fundamental solution of static equations of transversely isotropic plates. / I. P. Bokov, E. A. Strelnikova // International Journal of Innovative Research in Engineering & Management. – 2015. – Vol. 2, Issue-6. –P. 56–62.

Altuhov E. V. Kolivannya izotropnih plastin z urahuvannyam krayovih umov tipu ploskogo tortsya abo diafragmi / E. V. Altuhov, Yu. V. Panchenko, A. Yu. Bogatchuk // Visn. Donets. un-tu. Ser. A. Prirodnichi nauki. – 2000. – N 1. – S. 41–45.

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Published

2018-01-22

Issue

Vol. 20 No. 4 (2017)

Section

Dynamics and Strength of Machines

License

Copyright (c) 2018 Ю. Д. Ковалев, Е. А. Стрельникова, Д. В. Кушнир, Ю. В. Шрамко

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