SELF-OSCILLATIONS OF A LINEAR VISCOELASTIC ROD FREELY SUPPORTED AT THE ENDS

Authors

  • Mansurov Mukhsin Mannonovich Kokand State University

Keywords:

viscoelasticity, rod, self-oscillations, flutter, physical linearity, aerodynamic linearity, Bubnov-Galerkin method, relaxation kernel, numerical method, critical speed, linear integro-differential equation.

Abstract

This article considers the problem of self-oscillations (flutter) of a physically linear viscoelastic rod in a gas flow, taking into account linear dependencies. The statement and solution method of the problem of flutter of a viscoelastic rod simply supported at the ends are given.

References

Volmir A.S. Stability of Deformable Systems. Nauka Publishing House. Main Editorial Board of Physical and Mathematical Literature. Moscow, 1967

Volmir A.S. Nonlinear Dynamics of Plates and Shells. Nauka Publishing House. Main Editorial Board of Physical and Mathematical Literature. Moscow, 1972

Badalov F.B. Methods for Solving Integral and Integro-Differential Equations of the Hereditary Theory of Viscoelasticity. Tashkent, Mekhnat Publishing House, 1987. 269 p.

Badalov F.B. Method of Power Series in the Nonlinear Theory of Viscoelasticity. Tashkent, FAN 1980. 221 p.

Babakov I.M. Theory of Oscillations. Nauka Publishing House. Main Editorial Board of Physical and Mathematical Literature. Moscow, 1968.

Ilyushin A.A. Law of plane sections in aerodynamics of high supersonic speeds. PMM. 1956. Vol.20 No.6 p.733-755.

Eshmatov Kh.E., Nasretdinova Sh.S. Mathematical modeling of nonlinear problems of dynamics of viscoelastic systems. T., "Moliya", 2000, 108 p.

Timoshenko S.P. Stability of rods, plates and shells - M.: Nauka, 1971. - 807 p.

Galerkin, B.G. Rods and plates. Series in some questions of elastic equilibrium of rods and plates // Bulletin of Engineers. - 1915. - Vol.1, No.19. - P. 897-908.

Svetlitsky, V.A. Mechanics of rods. In 2 parts. - M.: Higher School, 1987. - 433p.

Badalov F.B., Ganikhanov Sh.F. Vibration of hereditarily deformable structural elements of aircraft. T., Tashkent State Aviation Institute, 2000, 141 p.

Abdikarimov R.A., Mansurov M.M., Akbarov U.Y. Numerical study of flutter of a viscoelastic rigidly clamped rod taking into account physical and aerodynamic nonlinearities. Bulletin of the Russian State University for the Humanities. Series "Computer Science. Information Security. Mathematics". Scientific journal. M., 3/2019, 94-106 p.

Abdikarimov R.A., Mansurov M.M., Pulatov Sh.Y. Influence of the rod shape on the critical flutter speed articulated at the ends. International Journal of Applied Research 2020. No.6(8), P.30-34.

Abdikarimov R.A., Akbarov U.Y., Pulatov Sh.Y., Mansurov M.M. Flutter of a viscoelastic rod hinged at the ends. Scientific and technical journal FerPI, 2020. Vol. 24, No. 3

Mansurov, M.; Abdikarimov, R.; Mirsaidov, M. Self-oscillatory process of a viscoelastic elongated plate; 2022; Construction of Unique Buildings and Structures; 100 Article No 10003. doi: 10.4123/CUBS.100.3

Mansurov M.M., Abdikarimov R.A., Kobilov M.Kh. Mathematical model of the problem of self-oscillations (flutter) of a viscoelastic rod taking into account physical and aerodynamic nonlinearities. Scientific and technical journal FerPI. Vol.28, Special issue No.7, pp. 9-15. 2024

Published

2025-06-11

How to Cite

Mansurov Mukhsin Mannonovich. (2025). SELF-OSCILLATIONS OF A LINEAR VISCOELASTIC ROD FREELY SUPPORTED AT THE ENDS. Ethiopian International Journal of Multidisciplinary Research, 12(06), 144–150. Retrieved from https://www.eijmr.org/index.php/eijmr/article/view/3273