# STEADY OSCILLATIONS OF A LAYER WEAKENED BY TWO HOLES, WITH THE ENDS COVERED WITH A DIAPHRAGM (SYMMETRIC CASE)

 DOI https://doi.org/10.15407/pmach2017.04.037 Journal Journal of Mechanical Engineering – Problemy Mashynobuduvannia Publisher A. Podgorny Institute for Mechanical Engineering Problems National Academy of Science of Ukraine ISSN 0131-2928 (Print), 2411-0779 (Online) Issue Vol. 20, no. 4, 2017 (December) Pages 37-44 Cited by J. of Mech. Eng., 2017, vol. 20, no. 4, pp. 37-44

Authors

Yu. D. Kovalev, Sumy State University (2, Rymskogo-Korsakova St., Sumy, 40007, Ukraine)

Ye. A. Strelnikova, A. Podgorny Institute of Mechanical Engineering Problems of NASU (2/10, Pozharsky St., Kharkiv, 61046, Ukraine), e-mail: elena15@gmx.com, ORCID: 0000-0003-0707-7214

D. V. Kushnir, Sumy State University (2, Rymskogo-Korsakova St., Sumy, 40007, Ukraine), e-mail: dmytro.kushnir@gmail.com

Yu. V. Shramko, Sumy State University (2, Rymskogo-Korsakova St., Sumy, 40007, Ukraine)

Abstract

This paper solves the problem of harmonic elastic oscillations of a layer with two through holes on whose surface a normal pulsating pressure acts. The boundary value problem is reduced to a system of integral equations, which is solved numerically. Examples are given, where the peculiarities of the distribution of circumferential voltage in frequency are investigated depending on the distance between the holes and Poisson’s ratio.

Keywords: harmonic oscillations, layer with two holes, integral equations

References

1.  Dawe, D. J. (2002). Use of the finite strip method in predicting the behaviour of composite laminated structures. Compos. Struct., vol. 57, iss. 1-4, pp. 11–36. https://doi.org/10.1016/S0263-8223(02)00059-4
2. Lure, A. I. (1942). K teorii tolstyih plit. Prikl. matematika i mehanika, vol. 6, iss. 2/3, pp. 151–168.
3. Kosmodamianskiy, A. S., & Shaldyirvan, V. A. (1978). Tolstyie mnogosvyaznyie plastinyi. Kyiv, Nauk. dumka, 240 p.
4. Shaldyrvan, V. A. &. Vasilev, T. A. (2005). The Lur’e-Vorovich Method in Mixed Problems of Bending of Cylindrical Bodies. International Applied Mechanics, vol. 41, iss. 8, pp. 882–889. https://doi.org/10.1007/s10778-005-0155-8
5. Altuhov, V. (1993). Uprugoe ravnovesie sloya s polostyu dlya granichnyih usloviy smeshannogo tipa na tortsah. Teoret. i prikl. Mehanika, iss. 24, pp. 3– 7.
6. Kosmodamianskii, A. S., Shaldyrvan, V. A., & Shaldyrvan, G. G. (1975). Stress concentration for the bending of a thick plate with an infinite series of cavities. Soviet Applied Mechanics, vol. 11, iss. 4, pp. 355–359. https://doi.org/10.1007/BF00882901
7. Filshtinskiy, L. A. & Kovalev, Yu. D. (2001). Smeshannaya kososimmetrichnaya zadacha ob uprugom sloe, oslablennom skvoznyimi polostyami. Fiziko-him. mehanika materialov – Physicochemical Mechanics of Materials, no. 5, pp. 114–116.
8. Filshtinskiy, A., Kovalyov, Yu. D., & Kushnir, D. V. (2004). Garmonicheskoe vozbuzhdenie uprugogo sloya s polostyu. Materialyi XIV Mezhdunar. nauchnoy shk. im. akademika S. A. Hristianovicha, Simferopol, pp. 151–153.
9. Bokov, P. & Strelnikova, E. A. (2015). Fundamental solution of static equations of transversely isotropic plates. International Journal of Innovative Research in Engineering & Management, vol. 2, iss. 6, pp. 56–62.
10. Altuhov, V., Panchenko, Yu. V., & Bogatchuk, A. Yu. (2000). Kolivannya izotropnih plastin z urahuvannyam krayovih umov tipu ploskogo tortsya abo diafragmi. Visn. Donets. un-tu. Ser. A. Prirodnichi nauki, no. 1, pp. 41–45.