Study of Stability of Cylindrical Shells Connected to an Annular Plate
Study of Stability of Cylindrical Shells Connected to an Annula
DOI:
https://doi.org/10.56143/ujmcs.v1i2.6Keywords:
construction; shell; deformation; relaxation; annular plate; stability; viscoelastic.Abstract
The paper presents the statement and methods for solving dynamic problems of multiply connected structurally inhomogeneous shell structures, which make it possible to reduce the problem of calculating a wide class of engineering structures to computer-aided design tasks. On the basis of numerical experiments and multi-parameter analysis of the system as a whole, a number of fundamentally important applied problems have been solved for calculating the dynamic characteristics of oscillations (frequencies, modes, determinant resonant amplitudes and damping coefficients) of special structures depending on the parameters of structural inhomogeneity. The stabilities of cylindrical shells connected to an annular plate under the action of dynamic loads are also considered. A methodics for comprehensive assessment of deformation properties is proposed in order to obtain the most rational mechanical and geometric characteristics based on mathematical modeling of deformation and relaxation processes.
References
[1] Urzhumtsev Yu.S., Mayboroda V.P.: Technical means and methods for determining the strength characteristics of polymer structures. M.: Engineering, 1984, 168 p.
[2] Kravchuk A.S., Mayboroda V.P., Urzhumtsev Yu.S.: Mechanics of Polymer and Composite Materials. Moscow (M): Nauka, 1985, 300 p.
[3] Filatov A.N.: Asymptotic methods in the theory of differential and integro-differential equations. Tashkent: FAN, 1974, 216 p.
[4] Koltunov M.A., Maiboroda V.P., Kravchuk A.S.: Applied mechanics of a deformable rigid body. M.: Higher School, 1983, 350 p.
[5] Koltunov M.A.: Creep and relaxation. M.: Higher School, 1976, 277 p.
[6] Ilyushin A.A., Pobedrya B.E.: Fundamentals of the mathematical theory of thermo-viscoelasticity. Moscow: Nauka, 1970, 280 p.
[7] Koltunov M.A., Mayboroda V.P., Zubchaninov V.G.: Strength calculations of products from polymeric materials. M.: Engineering, 1983, 239 p.
[8] Blend D.: Theory of linear viscoelasticity. M.: Mir, 1974, 338 p.
[9] Rzhanitsyn A.R.: Creep theory. M.: Stroyizdat, 1968, 416 p.
[10] Grigorenko Ya.M., Vasilenko A.T.: Methods for shell calculation. Vol. 4, Theory of shells of variable rigidity. Kiev: Naukova Dumka, 1981, 543 p.
[11] Karmishin A.V., Lyaskovets V.A., Myachenkov V.I., Frolov A.N.: Statics and dynamics of thin-walled shell structures. M.: Mechanical Engineering, 1975, 376 p.
[12] Myachenkov V.I., Maltsev V.P.: Methods and algorithms for the calculation of spatial structures at computer. M.: Mechanical Engineering, 1984, 278 p.
[13] Mirsaidov M.: Theory and methods for calculating earth structures for strength and rigidity. Tashkent: FAN, 2010, 312 p.
[14] Mirsaidov M., Godovannikov A.M.: Earthquake Resistance of Structures. Tashkent: Uzbekistan, 2008, 220 p.
[15] Sultanov K.S.: Wave theory of earthquake resistance of underground structures. Tashkent, 2016, 250 p.
[16] Sh. Salimov: IOP Conf. Ser.: Mater. Sci. Eng. 883, 012191 (2020).
[17] Sh. Salimov et al.: IOP Conf. Ser.: Mater. Sci. Eng. 883, 012192 (2020).
[18] Sh. M. Salimov, T. Mavlanov: IOP Conf. Ser.: Earth Environ. Sci. 614, 012057 (2020).
[19] Sh. M. Salimov et al.: “Solutions of vibration problems of structural-inhomogeneous shell structures by the M¨uller’s method”, AIP Conference Proceedings 2612, 020003 (2023). https://doi.org/10.1063/5.0124322
[20] Khudainazarov S. et al.: E3S Web of Conferences 365, 03040 (2023). https://doi.org/10.1051/e3sconf/202336503040
