Analytical and experimental investigation of free oscillations of open shells from alloy D19 carrying a system of attached masses

Deformable body mechanics


Sysoev O. E.*, Dobryshkin A. Y.**, Nein S. N.***

Komsomolsk-na-Amure State University, 27, Lenina str., Komsomolsk-on-Amur, 681013, Russia



Experimental studies have been carried out to determine the influence of the system of attached masses on the natural oscillations of shallow cylindrical shells of aluminum alloys, the results of which have been compared with theoretical calculations. The purpose of the experiment is to measure the free oscillations of an open, sloping cylindrical shell for various variations of the attached masses. Oscillations of an open, slender, thin-walled cylindrical shell, rectangular in plan, were measured using induction accelerometers. The theoretical calculation of the shell was carried out on the basis of the equations of motion of the theory of shallow shells, using the Bubnov-Galerkin method. A significant splitting of the flexural frequency spectrum is found, influenced not only by the systems of attached masses, but also by the values of the wave formation parameters, which depend on the relative geometric dimensions of the shell. The correspondence of analytical and experimental data is found, using the example of an open shell of alloy D19, which allows us to speak about the high quality of the study. A qualitative new analytical solution of the problem of determining the magnitude of the oscillation frequency of a shell carrying a system of attached masses is shown. For calculations, a hinged-supported open-shell model is used. The solution is based on the general equation of shell vibrations, a system of two differential equations describing small bending vibrations of the shell. On the basis of the general equation of oscillations of the shell (plate), an experimentally discrete nonlinear model of oscillations of a shallow shell bearing a system of attached masses with two degrees of freedom was obtained and confirmed experimentally. The experiment was carried out on a thin-walled cylindrical sloping open-shell model. The material of the sample is an aluminum alloy of the D-19 grade. Geometrical characteristics of the sample: R = 318 mm, L = 800 mm, H = 93 mm., δ = 0.4 mm. The shell is installed in a stand made in the laboratory of building structures. Experimental studies confirm theoretical studies. These studies can be used in the design of swimming machines, aircraft and other shells that have an attached mass. Carrying out of experimental studies has shown the validity of the obtained mathematical model, namely: the presence of a system of attached masses in an open cylindrical shell leads to splitting of the bending frequency spectrum of oscillations and the smaller of the split natural frequencies decreases at the same time.


hollow shell, nonlinear oscillations, stability model, adjoint mass


  1. Seregin S.V., Sysoev O.E. Materialy mezhdunarodnoi nauchno-prakticheskoi konferentsii “Deformirovanie i razrushenie kompozitsionnykh materialov i konstruktsii”, IMASh PAH, Moscow, 10-13 nojabrja 2014, pp. 22.

  2. Seregin S.V., Sysoev O.E. Materialy mezhdunarodnoi nauchno-prakticheskoi konferentsii “Zhivuchest’ i konstruktsionnoe materialovedenie”, IMASh PAH, Moscow, 21-23oktjabrja 2014, pp. 67.

  3. Shevchenko V.P., Vlasov O.I. Kairov V.A. Vіsnik Nacіonal’nogo tehnіchnogo unіversitetu Ukraїni, 2013, no. 2 (68), pp. 122 – 127.

  4. Sokolov V.G. Kolebaniya, staticheskaya i dinamicheskaya ustoichivost’ truboprovodov bol’shogo diametra (Fluctuations, static and dynamic stability of large-diameter pipelines), Doctor’s thesis, Saint-Petersburg, 2011, 287 p.

  5. Ivanov D.N., Naumova N.V., Sabaneev V.S., Tovstik P.E., Tovstik T.P. Vestnik Sankt-Peterburgskogo universiteta, 2016, vol. 3(61, no. 1, pp. 95 – 104.

  6. Lekomcev S.V Vychislitel’naya mekhanika sploshnykh sred, 2012, vol. 5, no. 2, pp. 233 – 243.

  7. Seregin S.V. Vychislitel’naya mekhanika sploshnykh sred, 2014, vol. 7, no. 4, pp. 378 – 384.

  8. Sysoev O.E, Dobryshkin A.Ju., Nejn S.N. Uchenye zapiski Komsomol’skogo-na-Amure gosudarstvennogo tekhnicheskogo universiteta, 2016, vol. 1, no. 3(27), pp. 110 – 116.

  9. Sysoev O.E., Dobryshkin A.Ju., Nejn S.N., Kahorov K.K.. Uchenye zapiski Komsomol’skogo-na-Amure gosudarstvennogo tekhnicheskogo universiteta, 2017, vol. 1, no. 1(29), pp. 110 – 118.

  10. Y. Qu, Y. Chen, X. Long, H. Hua, and G. Meng. Free and forced vibration analysis of uniform and stepped circular cylindrical shells using a domain decomposition method, Applied Acoustics, 2013, vol. 74, no. 3, pp. 425 – 439.

  11. Y. Qu, H. Hua, and G. Meng. A domain decomposition approach for vibration analysis of isotropic and composite cylindrical shells with arbitrary boundaries, Composite Structures, 2013, vol. 95, pp. 307 – 321.

  12. Y. Xing, B. Liu, and T. Xu. Exact solutions for free vibration of circular cylindrical shells with classical boundary conditions, International Journal of Mechanical Sciences, 2013. vol. 75, pp. 178 – 188.

  13. M. Chen, K. Xie, W. Jia, and K. Xu. Free and forced vibration of ring-stiffened conical–cylindrical shells with arbitrary boundary conditions, Ocean Engineering, 2015, vol. 108, pp. 241 – 256.

  14. H. Li, M. Zhu, Z. Xu, Z. Wang, and B. Wen. The influence on modal parameters of thin cylindrical shell under bolt looseness boundary, Shock and Vibration, 2016, vol. 2016, Article ID 4709257, 15 p.

  15. Foster N., Fernández–Galiano L. Norman Foster in the 21st Century, AV Monografías, Artes Gráficas Palermo, 2013. pp. 163 – 164.

  16. Eliseev V.V., Moskalets A.A., Oborin E.A. One-dimensional models in turbine blades dynamics, Lecture Notes in Mechanical Engineering, 2016, vol. 9, pp. 93 – 104.

  17. Hautsch N., Okhrin O., Ristig A. Efficient iterative maximum likelihood estimation of highparameterized time series models, Berlin, Humboldt University, 2014, 34 p.

  18. Belostochnyj G.N., Myl’cina O.A. Trudy MAI, 2015, no. 82, available at:

  19. Kuznecova E.L., Tarlakovskij D.V., Fedotenkov G.V., Medvedskij A.L. Trudy MAI, 2013, no. 71, available at:

  20. Demin A.A., Golubeva T.N., Demina A.S. The program complex for research of fluctuations’ ranges of plates and shells in magnetic field, 11th Students’ Science Conference “Future Information technology solutions”, Bedlewo, 3-6 October 2013, pp. 61 – 66.

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