Structural Mechanics of Engineering Constructions and BuildingsStructural Mechanics of Engineering Constructions and Buildings1815-52352587-8700Peoples’ Friendship University of Russia (RUDN University)2072010.22363/1815-5235-2019-15-1-69-74Research ArticleAsymptotic analysis of natural frequencies of axisymmetric oscillations of orthotropic cylindrical shells in an infinite elastic medium, liquid filledSeyfullayevFamil A<p>PhD in Technical Sciences, Senior Researcher Fellow, Department of Wave Dynamics, Institute of Mathematics and Mechanics</p>a.seyfullayev@yahoo.comMirzayevaGulnar R<p>PhD in Technical Sciences, Senior Researcher Fellow, Department of Wave Dynamics, Institute of Mathematics and Mechanics</p>gulnar.mirzayeva@gmail.comKerimovaShusha A<p>researcher, Department of Wave Dynamics, Institute of Mathematics and Mechanics</p>shusha_az@rambler.ruAzerbaijan National Academy of Sciences15122019151697413032019Copyright © 2019, Seyfullayev F.A., Mirzayeva G.R., Kerimova S.A.2019<p>Aim of the research. Free axisymmetric fluctuation of a cylindrical orthotropic cover, the infinite length contacting to the infinite elastic medium and filled with liquid is investigated. Methods. At design of the thin-walled shell designs which are widely applied in aviation, the missile and space equipment and various fields of the industry, an important task is dynamic calculation of the intense deformed condition of these designs. At a research of dynamics of covers it is necessary to determine own frequencies and forms of small fluctuations, and frequencies from the lower part of a range are of the greatest interest. It is supposed that the rigidity of material of a cover is a little more than rigidity of material of the environment. The solution of the equations of movements of the environment is considered in two options. Results. The frequency equation is received. The analysis of frequency and a form of fluctuations of a cover is carried out. The schedule of dependence of frequency of own axisymmetric fluctuations of a system on wave formation in the longitudinal direction is constructed. By means of an asymptotic method the frequency equations of the ridge cylindrical covers filled with liquid are constructed, the approximate frequencies of the equation and simple settlement formulas allowing to find values of the minimum own frequencies of fluctuations of the considered system are received, the forced fluctuations of the supported cover filled with liquid are investigated and defined is amplitude frequency characteristics of the considered oscillatory processes.</p>orthotropic shellfree vibrationsnatural oscillation frequencieswave formationelastic environmentортотропная оболочкасвободные колебаниясобственные частоты колебанияволнообразованиеупругая среда[Latifov F.S., Seyfullaev F.A., Alyev Sh.Sh. (2016). Svobodnye kolebaniya usilennoj poperechnymi rebrami anizotropnoj cilindricheskoj obolochki iz stekloplastika s tekushchej v nej zhidkost'yu [Free vibrations reinforced by transverse ribs of an anisotropic cylindrical shell made of fiberglass with a liquid flowing in it]. Applied mechanics and technical physics, 57(4), 158–162. (In Russ.)][Latifov F.S., Seyfullayev F.A. (2004). Asymptotic analysis of oscillation eigenfrequency of orthotropic cylindrical shells in infinite elastic medium filled with liquid. Trans. NAS Acad. Azer. Ser. Phys.-Tech. Math. Sci., 24(1), 227–230.][Bosiakov S.M., Zhiwei W. (2011). Analiz svobodnyh kolebanij cilindricheskoj obolochki iz stekloplastika pri granichnyh usloviyah Nav'e [Free vibration analysis of cylindrical shell from fiberglass with Navier boundary conditions]. Mechanics of machines, mechanisms and materials, (3), 24–27. (In Russ.)][Semenov A.A. (2016). Model of deformation stiffened orthotropic shells under dynamic loading. Journal of Siberian Federal University. Mathematics and Physic, 9(4), 485–497.][Seyfullayev A.I., Novruzova K.A. (2015). Issledovanie kolebaniya prodol'no podkreplennoj ortotropnoj cilindricheskoj obolochki s vyazkoj zhidkost'yu [Oscillations of longitudinally reinforced orthotropic cylindrical shell filled with a viscous fluid]. Eastern-European Journal of Enterprise Technologies, 3/7(75), 29–33 (In Russ.)][Kolosov G.I. (2012). Vibracionnaya i vekovaya neustojchivost' sostoyanij ravnovesiya cilindricheskih obolochek pri osevom szhatii [Vibration and secular instability of equilibrium states of cylindrical shells under axial compression]. Cosmonovtika i raketostroenie, 2(67), 145–150. (In Russ.)][Obukhov A.S. (1978). Raschyot na prochnost' konstrukcij iz stekloplastikov i plastmassa neftepererabatyvayushchej i himicheskoj promyshlennosti [Calculation of the strength of structures made of fiberglass and plastic of the oil refining and chemical industries]. Moscow: Mashinostroenie Publ., 141. (In Russ.)][Latifov F.S. (1999). Kolebaniya obolochek s uprugoj i zhidkoj sredoj [Oscillations of shells with elastic and liquid media]. Baku: Elm Publ., 164. (In Russ.)][Smirnov V. (1974). Kurs vysshej matematiki [Course of Higher Mathematics]. Vol. 3. Part 2. Moscow: Nauka Publ., 672. (In Russ.)][Seyfullayev A.I., Rustamova M.A., Kerimova Sh.A. (2017). Zadacha mekhaniki ustalostnogo razrusheniya dvuhslojnogo materiala s kraevymi treshchinami [Problem of the mechanics of fatigue fracture of a two-layer material with edge cracks]. Mechanics of Composite Material, 53(3), 415–424. (In Russ.)][Akbarov S.D., Guliev M.S. (2008). Propagation of axisymmetric longitudinal waves in a finitely pre-strained circular cylinder embedded in a finitely pre-strained infinite elastic body. Mechanics of Composite Materials, 44(5), 465–478. doi.org/10.1007/s11029-008-9045-6][Akbarov S.D. (2007). Resent investigations on the dynamical problems of the elastic body with initial (residual) stresses (review). Int. Appl. Mechanic, 43(12), 3–27.][Agalarov J.G., Seyfullayev A.I., Rustamova M.A. (2017). Dvizhenie vertikal'no raspolozhennogo cilindra v rezul'tate voln na poverhnosti zhidkosti [The movement of vertically located cylinder as a result of waves on the surface of liquid]. Bulletin of Modern Science, 2(26), 7–15. (In Russ.)][Bochkarev S.A., Matveenko V.P. (2006). Konechnoehlementnyj analiz sobstvennyh kolebanij cilindricheskoj obolochki s zhidkost'yu [Finite-element analysis of natural oscillations of a cylindrical shell with a liquid]. Vychisl. mechanics: collection of scientific works, (4), 3–12. Perm: Perm State Technical University Publ. (In Russ.)][Latifov F.S. (1999). Asimptoticheskij analiz zadachi o svobodnyh neosesimmetrichnyh kolebaniyah v beskonechnoj uprugoj srede cilindricheskoj obolochki, zapolnennoj ideal'noj zhidkost'yu [The asymptotic analysis of a task about free not axisymmetric fluctuations in an infinite elastic medium of the cylindrical cover filled with ideal liquid]. DAN Az. Republics, LV(5–6), 8–15. (In Russ.)]