|Journal||Journal of Mechanical Engineering – Problemy Mashynobuduvannia|
|Publisher||A. Pidhornyi Institute for Mechanical Engineering Problems
National Academy of Science of Ukraine
|ISSN||2709-2984 (Print), 2709-2992 (Online)|
|Issue||Vol. 25, no. 1, 2022 (March)|
|Cited by||J. of Mech. Eng., 2022, vol. 25, no. 1, pp. 6-14|
A mathematical model of the dynamic instability of a three-layer conical shells with honeycomb structure made using additive technologies has been obtained. Dynamic instability is recognized as the interaction of the shell with a supersonic gas flow. The middle layer of the structure is a honeycomb that is homogenized into an orthotropic homogeneous medium. The top and bottom layers of the shell are made of carbon fiber. The vibrations of the structure are described by fifteen unknowns. Each layer of the structure is described by five unknowns: three projections of displacements of the layer middle surface and two rotation angles of the normal of the layer middle surface. The high-order shear theory is used to describe the deformation state of the structure. The relation between stresses and strains is expressed by a power expansion in the transverse coordinate up to its cubic terms. To obtain a system of ordinary differential equations describing dynamic instability, the method of given forms is used. To assess the dynamic instability, characteristic indicators are calculated by solving the generalized problem of eigenvalues. The natural vibrations of the structure are studied by the Rayleigh-Ritz method. The minimum natural frequency in the cantilevered shell is observed when the number of waves in the circumferential direction is 6. It is also observed in the shell clamped on both sides when the number of waves in the circumferential direction is 1. The dynamic instability properties of the trivial equilibrium state of the structure are studied using numerical simulation. Shells that are cantilevered and clamped on both sides are analyzed. It is shown that the minimum critical pressure is observed when the number of waves in the circumferential direction is 1. The dependence of the critical pressure on the Mach number and angle of attack is studied. It has been established that with an increase in the Mach number and angle of attack, the critical pressure decreases.
Keywords: linear dynamic system, three-layer conical shell, characteristic exponents, Mach numbers.
Full text: Download in PDF
- Karimiasl, M. & Ebrahimi, F. (2019). Large amplitude vibration of visco-elastically damped multiscale composite doubly curved sandwich shell with flexible core and MR layers. Thin-Walled Structures, vol. 144, paper ID 106128. https://doi.org/10.1016/j.tws.2019.04.020.
- Karimiasla, M., Ebrahimia, F., & Maheshb, V. (2019). Nonlinear forced vibration of smart multiscale sandwich composite doubly curved porous shell. Thin-Walled Structures, vol. 143, paper ID 106152. https://doi.org/10.1016/j.tws.2019.04.044.
- Cong, P. H., Khanh, N. D., Khoa, N. D., & Duc, N. D. (2018). New approach to investigate nonlinear dynamic response of sandwich auxetic double curves shallow shells using TSDT. Composite Structures, vol. 185, pp. 455–465. https://doi.org/10.1016/j.compstruct.2017.11.047.
- Yadav, A., Amabili, M., Panda, S. K., Dey, T., & Kumar, R. (2021). Forced nonlinear vibrations of circular cylindrical sandwich shells with cellular core using higher-order shear and thickness deformation theory. Journal of Sound and Vibration, vol. 510, paper ID 116283. https://doi.org/10.1016/j.jsv.2021.116283.
- Van Quyen, N., Thanh, N. V., Quan, T. Q., & Duc, N. D. (2021). Nonlinear forced vibration of sandwich cylindrical panel with negative Poisson’s ratio auxetic honeycombs core and CNTRC face sheets. Thin-Walled Structures, vol. 162, paper ID 107571. https://doi.org/10.1016/j.tws.2021.107571.
- Zhang, Y. & Li, Y. (2019). Nonlinear dynamic analysis of a double curvature honeycomb sandwich shell with simply supported boundaries by the homotopy analysis method. Composite Structures, vol. 221, paper ID 110884. https://doi.org/10.1016/j.compstruct.2019.04.056.
- Naidu, N. V. S. & Sinha, P. K. (2007). Nonlinear free vibration analysis of laminated composite shells in hygrothermal environments. Composite Structures, vol. 77, iss. 4, pp. 475–483. https://doi.org/10.1016/j.compstruct.2005.08.002.
- Catapano, A. & Montemurro, M. (2014). A multi-scale approach for the optimum design of sandwich plates with honeycomb core. Part I: homogenisation of core properties. Composite Structure, vol. 118, pp. 664–676. https://doi.org/10.1016/j.compstruct.2014.07.057.
- Amabili, M. (2018). Nonlinear mechanics of shells and plates in composite, soft and biological materials. United Kingdom, Cambridge: Cambridge University Press, 568 p. https://doi.org/10.1017/9781316422892.
- Meirovitch, L. (2001). Fundamentals of vibrations. New York: Mc Graw Hill Press, 806 p. https://doi.org/10.1115/1.1421112.
- Amabili, M. (2015). Non-linearities in rotation and thickness deformation in a new third-order thickness deformation theory for static and dynamic analysis of isotropic and laminated doubly curved shells. International Journal of Non-Linear Mechanics, vol. 69, pp. 109–128. https://doi.org/10.1016/j.ijnonlinmec.2014.11.026.
- Derevianko, I., Avramov, K., Uspenskyi, B., & Salenko, A. (2021). Eksperymentalnyi analiz mekhanichnykh kharakterystyk detalei raket-nosiiv, vyhotovlenykh za dopomohoiu FDM adytyvnykh tekhnolohii [Experimental analysis of mechanical characteristics of parts of launch vehicles manufactured using FDM additive technologies]. Tekhnichna mekhanika – Technical Mechanics, iss. 1, pp. 92–100 (in Ukrainian). https://doi.org/10.15407/itm2021.01.092.
Received 11 January 2022
Published 30 March 2022