Abstract
For the first time, the equations of aeroelastic stability of a composite cylindrical shell of linearly varying thickness are obtained on the basis of the bending theory of orthotropic shells under loading with axial forces and supersonic gas flow. The solution to the equations is sought in the form of trigonometric series along the axial coordinate. The problem is reduced to an infinite system of algebraic equations by the Bubnov–Galerkin method. The characteristic equation obtained is approximated by the Lagrange polynomial, the stability of which is investigated using the Routh–Hurwitz criterion. By a numerical example, the effect of the thickness gradient, structural damping, and axial force on the critical velocity when flow by a supersonic gas around а shell of linearly varying thickness is shown. The refinement of the results of calculations carried out with the model developed amounted to almost 35% for the critical velocities as compared to those found from the model for a shell with an average thickness, which evidences the urgency of the problem solved for weight perfection of aircrafts. The approach proposed significantly extends the range of problems to be solved and allows calculating the aeroelastic stability of orthotropic cylindrical shells of linearly varying thickness in the flow around by the supersonic gas flow.
Similar content being viewed by others
REFERENCES
A. V. Lipanov and A. V. Aliev, SPRE Design (Mashinostroenie, Moscow, 1995) [in Russian].
V. N. Bakulin, I. F. Obraztsov, and V. A. Potopakhin, Dynamic Problems of Nonlinear Theory of Multilayer Shells: Action of Intense Thermal-Force Loads and Concentrated Energy Fluxes (Fizmatlit, Moscow, 1998) [in Russian].
V. N. Bakulin, Probl. Prochn., No. 5, 78 (1985).
V. N. Bakulin and D. A. Mysyk, Mekh. Kompoz. Mater., No. 5, 933 (1980).
V. N. Bakulin, A. Ya. Nedbai, and I. O. Shepeleva, Russ. Aeronaut. 62 (2), 192 (2019).
S. D. Algazin and I. A. Kiiko, Flutter of Plates and Shells (Nauka, Moscow, 2006) [in Russian].
V. N. Bakulin, E. N. Volkov, and A. Ya. Nedbay, Dokl. Phys. 60 (8), 360 (2015).
V. N. Bakulin, E. N. Volkov, and A. Ya. Nedbai, Journal of Engineering Physics and Thermophysics. 89 (3), 747 (2016).
V. N. Bakulin, M. A. Bokov, and A. Ya. Nedbay, Mechanics of Composite Materials. 53 (6), 801 (2018).
V. N. Bakulin, E. N. Volkov, and A. I. Simonov, Russ. Aeronaut. 60 (4), 508 (2017).
V. N. Bakulin, E. V. Danilkin, and A. Ya. Nedbay, Journal of Engineering Physics and Thermophysics. 91 (2), 537 (2018).
V. N. Bakulin, M. A. Konopel’chev, and A. Ya. Nedbai, Russ. Aeronaut. 61 (4), 517 (2018).
Yu. S. Solomonov, V. P. Georgievskii, and A. Ya. Nedbay, Mekh. Kompoz. Mater. i Konstr., No. 3, 435 (2017).
V. G. Moskvin, Proc. 8th All-Union Conf. on Theory of Shells and Plates (Nauka, Moscow, 1962), pp. 527–531 [in Russian].
Yu. S. Solomonov, V. P. Georgievskii, A. Ya. Nedbay, and V. A. Andryushin, Applied Problems of Mechanics of Composite Cylindrical Shells (Fizmatlit, Moscow, 2014) [in Russian].
Funding
The work has been performed under the state order. Official registration number: AAAA - A19-119012290177-0.
Author information
Authors and Affiliations
Corresponding authors
Additional information
Translated by V. Bukhanov
Rights and permissions
About this article
Cite this article
Bakulin, V.N., Konopelchev, M.A. & Nedbay, A.Y. Aeroelastic Stability of a Cylindrical Shell of Linearly Varying Thickness. Dokl. Phys. 64, 360–364 (2019). https://doi.org/10.1134/S1028335819090015
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1028335819090015