DOI
10.34229/KCA2522-9664.25.2.16
UDC 519.6, 539.3
1 State University of Intellectual Technologies and Communication, Odesa, Ukraine
 kovalevurad@ukr.net
|
|
MODELING OF IMPULSE EXCITATION OF A LAYER WEAKENED
BY A THROUGH HOLE (SKEW-SYMMETRIC CASE)
Abstract. The paper considers a new mathematical model for solving a dynamic (shock) skew-symmetric boundary-value problem
for a layer weakened by a through hole with sliding sealing of its ends.
A new method based on the system of 3k (k = 1,2,...) singular integral equations
of the 2nd kind is developed and tested numerically. A highly accurate numerical study demonstrated that the relative
circumferential stress increases with an increase in the impulse length. Short impulses result in a wave-like fading process,
i.e., in the ε -neighborhood of the origin, due to the inertia of the system, a zone of negative stresses appears, which, interacting with a positive impulse, give rise to this process. A similar situation is observed when the impulse is removed. The corresponding graphs are shown.
Keywords: three-dimensional non-stationary dynamic boundary-value problems, singular integral equations, numerical experiment, impulse bend, through hole.
full text
REFERENCES
- 1. Shevchenko V.P., Altukhov E.V., Fomenko M.V. Deformation of three-layer plates with sliding sealing of ends and imperfect contact of layers. Dop. Dop. NAS of Ukraine. 2012. N 8. P. 61–66.
- 2. Spatial problems of the theory of elasticity and plasticity. In 6 volumes (Ed. A. N. Guz). K.: Nauk. dumka, 1984–1986. Vol. 2. Guz A. N., Nemish Yu. N. Statics of elastic bodies of non-canonical shape, 1984. 280 p.
- 3. Altukhov E.V., Fomenko M.V. Oscillations of three-layer plates with rigid end-capping and with layer slippage. Teor. i prikl. mekh. 2011. Iss. 3 (49). P. 38—50.
- 4. Shevchenko V.P., Altukhov E.V., Fomenko M.V. Elastic vibrations of three-layer plates in the case of a flat end face. Dop. NAS of Ukraine. 2011. N 9. P. 70–77. http://dspace.nbuv.gov.ua/handle
- 5. Filshtinsky L.A., Kovalev Yu.D. Bending vibrations of a layer with tunnel holes during sliding sealing of its ends. "CONSONANCE-2003" Acoustic Symposium (1–3 October 2003) Kyiv: Institute of Hydromechanics of the National Academy of Sciences of Ukraine, 2003. P. 265–270.
- 6. Belotserkovskii S.M., Lifanov I.K. Numerical methods in singular integral equations and their application in aerodynamics, elasticity theory, electrodynamics. Moscow: Nauka, 1985. 235 p.
- 7. Panchenko B.E., Kovalev Yu.D., Kalinina T.O., Saiko I.N., Bukata L.M. Mathematical modeling in static three-dimensional boundary-value problems: A skew-symmetric problem for a layer weakened by a through hole sliding and clamping. Cybernetics and Systems Analysis. 2024. Vol. 60, N 1. P. 152–162. https://doi.org/10.1007/s10559-024-00656-9.
