VISUALIZATION OF SCENARIOS FOR THE TRANSITION OF OSCILLATIONS FROM HARMONIC TO CHAOTIC FOR A MICROPOLAR KIRCHHOFF-LOVE CYLINDRICAL MESHED PANEL
Аннотация и ключевые слова
Аннотация (русский):
On the basis of the kinematic hypotheses of the Kirchhoff-Love built a mathematical model of micropolar cylindrical meshed panels vibrations under the action of a normal distributed load. In order to take into account the size-dependent behavior, the panel material is considered as a Cosser’s pseudocontinuum with constrained particle rotation. The mesh structure is taken into account by the phenomenological continuum model of G. I. Pshenichnov. For a cylindrical panel consisting of two systems of mutually perpendicular edges, a scenario of transition of oscillations from harmonic to chaotic is constructed. It is shown that in the study of the behavior of cylindrical micropolar meshed panels it is necessary to study the nature of the oscillations of longitudinal waves.

Ключевые слова:
visualization of scenarios for the transition of oscillations into chaos, a mesh structure, a cylindrical panel, micropolartheory, the Kirchhoff-Love model
Список литературы

1. Azarov A.V. Continuum model of composite mesh shellsformed by a system of spiral edges // Composites andnanostructures. 2015. Vol. 7. № 3 (27). P. 151-161. (in Russian)

2. Azikov N. With. Pavlov E. A. stability Study of a meshcomposite plate //Aviation industry. 2016. № 3. P. 46-50. (inRussian)

3. Belikov G. I. General case of bending of a rectangular meshplate taking into account the tensile forces acting in the middlesurface // Bulletin of the Volgograd state University ofarchitecture and civil engineering. Series: Construction andarchitecture. 2014. № 37 (56). P. 121-128. (in Russian)

4. Burnysheva T. V., Kaledin V. O. Comparison of discreteand continuous approach to the calculation of the stress state ofmesh shell structures under static loading //Journal Scientific andtechnical of the Volga region. 2011. № 4. P. 113-116. (inRussian)

5. Burnysheva T. V., Steinbrecher, O. A., Ulyanov A. D.Aspects of specifying boundary conditions in the simulationmesh anisogamy designs // Bulletin of the South Ural stateUniversity. Series: Mathematical modeling and programming.2018. V. 11. № 1. P. 137-144. (in Russian)

6. Eremeev V. A On a nonlinear model of the mesh shell //Izvestiya of the Russian Academy of Sciences. Solid mechanics.2018. № 4. P. 127-133 (in Russian)

7. Zinin A.V., Azik N. With. The model of destruction processof composite structures anisakidae problems //Mechanicalengineering and reliability of machines.2018. № 5. С. 49-56. (inRussian)

8. E. Yu. Krylova, V. I. Papkova, O. A. Saltykova, O. A.Sinichkina, Krys'ko V. A. Mathematical model of thefluctuations of the size-dependent cylindrical shells meshstructure given the hypotheses of the Kirchhoff-Love //non-linearworld. 2018. Vol. 16. № 4. P. 17-28(in Russian)

9. Krylov E. Y., Papkova I. V., Saltykova, O. A., YakovlevaT. V., Krysko V. A.-jr Analysis of the natural frequencies of themicropolar, mesh for cylindrical panel of the Kirchhoff-love Inthe collection: Problems of mechanical engineering proceedingsof the III International scientific-technical conference. In 2 parts.Scientific editor P. D. Balakin. 2019. P. 278-282.(in Russian)

10. NikabadzeM.U. Some variants of the equations of themicropolar theory of shells Applied mathematics andmathematical physics.2015. Vol. 1. № 1. P. 101-118. (inRussian)

11. Trushin S.I., Zhuravleva T.A., Sysoeva E.V. Dynamic lossof stability of nonlinear deformable grid plates made ofcomposite material with different lattice configurations //Scientific review. 2016. No. 4. P. 44-51.

12. Awrejcewicz J., Krysko V.A., Sopenko A.A., ZhigalovM.V., Kirichenko A.V., Krysko A.V. Mathematical modelling ofphysically/geometrically non-linear micro-shells with account ofcoupling of temperature and deformation fields // Chaos, Solitons& Fractals. 2017. V. 104. P. 635-654.

13. Awrejcewicz J., Mrozowski J., Krysko A.V., Papkova I.V.,Zakharov V.M., Erofeev N.P., Krylova E.Y., Krysko V.A.Chaotic dynamics of flexible beams driven by external whitenoise //Mechanical Systems and Signal Processing. 2016. Т. 79.С. 225-253.

14. Krylova E Y, Papkova I V, Erofeev N P, Zakharov V M,Krysko V A Сomplex fluctuations of flexible plates underlongitudinal loads with account for white noise // Journal ofApplied Mechanics and Technical Physics. 2016. V. 57. № 4. P.714-719.

15. Krylova E Yu, Papkova I V, Sinichkina A O, Yakovleva TB, Krysko-yang V A Mathematical model of flexible dimensiondependent mesh plates // IOP Conf. Series: Journal of Physics:Conf. Series 1210 (2019) 012073 doi:10.1088/1742-6596/1210/1/012073

16. Krysko V A, Papkova I V, Awrejcewicz J, Krylova E Y,Krysko A V Non-symmetric forms of non-linear vibrations offlexible cylindrical panels and plates under longitudinal load andadditive white noise // Journal of Sound and Vibration. 2018. V.423. P. 212-229.

17. Safarpour H., Mohammadi K. and Ghadiri M. Temperaturedependent vibration analysis of a FG viscoelastic cylindricalmicroshell under various thermal distribution via modified lengthscale parameter: a numerical solution // Journal of theMechanical Behavior of Materials 2017, Volume 26, Issue 1-2,Pages 9–24

18. Sahmani S., Ansari R., Gholami, R., Darvizeh A. Dynamicstability analysis of functionally graded higher-order sheardeformable microshells based on the modified couple stresselasticity theory //Composites Part B Engineering 51 (2013) 44–53

19. Sargsyan S.H., Zhamakochyan K.A. Applied theory ofmicropolar elastic thin plates with constrained rotation and thefinite element method// Materials Physics and Mechanics. 2018.Т. 35. № 1. С. 145-154

20. Scheible D. V., Erbe A., Blick R. H. Evidence of ananomechanical resonator being driven into chaotic responseviathe Ruelle–Takens route // Appl. Phys. Lett. 81 (2002), 1884–1886.

21. Varygina M. Numerical modeling of micropolar cylindricalshells on supercomputers with GPUs // AIP ConferenceProceedings 1895, 080005 (2017)

22. Xinping Zhou Lin Wang Vibration and stability of microscale cylindrical shells conveying fluid based on modified couplestress theory Micro & Nano Letters 2012 Volume: 7 , Issue: 7 ,p 679 – 684

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