TECHNICAL MECHANICS
ISSN (Print): 1561-9184, ISSN (Online): 2616-6380

English
Russian
Ukrainian
Home > Journal Issues > No 2 (2022) Technical mechanics > 8
___________________________________________________

UDC 539.3

Technical mechanics, 2022, 2, 87 - 100

Self-vibrations of a truncated conical sandwich shell with a honeycomb core made by additive technologies

Avramov K. V., Uspensky B. V.

      ABOUT THE AUTHORS

Avramov K. V.
A. Pidgorny Institute of Mechanical Engineering Problems of the National Academy of Sciences of Ukraine
Kharkiv National University of Radio Electronics

Uspensky B. V.
A. Pidgorny Institute of Mechanical Engineering Problems of the National Academy of Sciences of Ukraine

      ABSTRACT

      This paper presents a nonlinear mathematical model of self-vibrations of conical sandwich shells with a honeycomb core made by additive technologies. The vibrations of the structure are described by fifteen unknowns. Each layer of the structure is described by five unknowns: three projections of the displacements of the layer middle surface and two rotation angles of the middle surface normal. Displacement continuity conditions at the layer interfaces are used. The higher-order shear theory is used to describe the stress-strain state of the structure. The case of conical sandwich shell ? supersonic gas flow interaction is considered. Due to this interaction, self-vibrations of the shell structure are set up. In their analysis, the geometrical nonlinearity of the structure is accounted for. Motion equations of the structure are derived using the assumed-mode method, which uses the kinetic and the potential energy of the structure. The self-vibrations are represented as eigenmode expansions, which contain a set of generalized coordinates. A system of nonlinear autonomous ordinary differential equations in the generalized coordinates is derived. The self-vibrations are studied using a combination of the shooting technique and the parameter continuation method. Multipliers are calculated to analyze the stability of periodic vibrations and their bifurcations. The dynamic instability of the structures trivial equilibrium is studied by numerical simulation. For clamped-clamped and cantilever shells, the properties of their periodic, quasiperiodic, and chaotic motions are analyzed in detail.
      Pdf (English)







      KEYWORDS

nonlinear dynamical system, conical sandwich shell, self- sustained vibrations, quasiperiodic vibrations, chaos

      FULL TEXT:

Pdf (English)









      REFERENCES

1. Karimiasl M., Ebrahimi F. Large amplitude vibration of viscoelastically damped multiscale composite doubly curved sandwich shell with flexible core and MR layers. Thin-Walled Structures. 2019. V. 144. 106128. https://doi.org/10.1016/j.tws.2019.04.020

2. Karimiasla M., Ebrahimia F., Maheshb V. Nonlinear forced vibration of smart multiscale sandwich composite doubly curved porous shell. Thin-Walled Structures. 2019. V. 143. 106152. https://doi.org/10.1016/j.tws.2019.04.044

3. Cong P. H., Khanh N. D., Khoa N. D., Duc N. D. New approach to investigate nonlinear dynamic response of sandwich auxetic double curves shallow shells using TSDT. Composite Structures. 2018. V. 185. Pp. 455-465. https://doi.org/10.1016/j.compstruct.2017.11.047

4. Yadav A., Amabili M., Panda S. K., Dey T., Kumar R. Forced nonlinear vibrations of circular cylindrical sandwich shells with cellular core using higher-order shear and thickness deformation theory. Journal of Sound and Vibration. 2021. V. 510. 116283. https://doi.org/10.1016/j.jsv.2021.116283

5. Van Quyen N., Thanh N. V., Quan T. Q., Duc N. D. Nonlinear forced vibration of sandwich cylindrical panel with negative Poisson's ratio auxetic honeycombs core and CNTRC face sheets. Thin-Walled Structures. 2021. V. 162. 107571. https://doi.org/10.1016/j.tws.2021.107571

6. Zhang Y., Li Y. Nonlinear dynamic analysis of a double curvature honeycomb sandwich shell with simply supported boundaries by the homotopy analysis method. Composite Structures. 2019. V. 221. 110884. https://doi.org/10.1016/j.compstruct.2019.04.056

7. Naidu N. V. S., Sinha P. K. Nonlinear free vibration analysis of laminated composite shells in hygrothermal environments. Composite Structures. 2007. V. 77. Pp. 475-483. https://doi.org/10.1016/j.compstruct.2005.08.002

8. Li C., Shen H.-S., Wang H., Yu Z. Large amplitude vibration of sandwich plates with functionally graded auxetic 3D lattice core. International Journal of Mechanical Sciences. 2020. V. 174. 105472. https://doi.org/10.1016/j.ijmecsci.2020.105472

9. Hudramovich V. S., Demenkov A. F. Elastoplastic Structures with Shape Imperfections and Residual Stresses. Kyiv: Naukova Dumka, 1991. 176 pp. (in Russian).

10. Hudramovich V. S., Skalskyi V. R., Selivanov Yu. M. Holographic and Acoustic-Emissive Diagnostics of Structures and Materials. Z. T. Nazarchiuk (Ed.). Lviv: Prostir-M, 2017. 492 pp. (in Ukrainian).

11. Hudramovich V. S. Strength, reliability, and life of aerospace and power engineering structures. Teh. Meh. 2021. No. 2. Pp. 100-106. (in Ukrainian). https://doi.org/10.15407/itm2021.02.100

12. Catapano A., Montemurro M. A multi-scale approach for the optimum design of sandwich plates with honeycomb core. Part I: homogenisation of core properties. Comp. Struct. 2014. V. 118. Pp. 664-676. https://doi.org/10.1016/j.compstruct.2014.07.057

13. Grediac M. A finite element study of the transverse shear in honeycomb cores. Int. J. of Solids and Struc. 1993. V. 30. Pp. 1777-1788. https://doi.org/10.1016/0020-7683(93)90233-W

14. Novozhilov V. V. Foundations of Nonlinear Elasticity Theory. Moscow: OGIZ, 1948. 211 pp. (in Russian).

15. Bakhtiari M., Lakis A. A., Kerboua Y. Nonlinear supersonic flutter of truncated conical shells. Journal of Mechanical Science and Technology. 2020. V. 34. No. 4. Pp. 1375-1388. https://doi.org/10.1007/s12206-020-0301-6

16. Meirovitch L. Fundamentals of Vibrations. 2001. Mc Graw Hill. 826 pp.

17. Amabili M. Nonlinear Mechanics of Shells and Plates in Composite, Soft and Biological Materials. Cambridge University Press, 2018. https://doi.org/10.1017/9781316422892

18. Avramov K. V., Mikhlin Yu. V. Nonlinear Dynamics of Elastic Systems. V. 1. Models, Methods, and Phenomena. Moscow: Research Center "Regular and Chaotic Dynamics", 2010. 704 pp. (in Russian).

19. Derevianko I., Avramov K., Uspensky B., Salenko A. Experimental analysis of the mechanical characteristics of launch vehicle parts manufactured by FDM additive technologies. Teh. Meh. 2021. No. 1. Pp 92-100. (in Ukrainian). https://doi.org/10.15407/itm2021.01.092





Copyright () 2022 Avramov K. V., Uspensky B. V.

Copyright 2014-2022 Technical mechanics


____________________________________________________________________________________________________________________________
GUIDE
FOR AUTHORS
Guide for Authors ==================== Open Access Policy
Open Access Policy ==================== REGULATIONS
on the ethics of publications
REGULATIONS on the ethics of publications ====================