Skip to main content
Log in

Natural Vibrations of a Cylindrical Shell Reinforced with Two-Layer Rings

  • Published:
International Applied Mechanics Aims and scope

Abstract

The vibrations of a cylindrical shell reinforced with ring ribs attached to the shell by means of elastic elements are studied. The problem is solved by the finite-element method. The shell and ribs are modelled by a plane four-node finite element, which is a combination of a four-node plane stress element and a four-node flexural element. The effect of the stiffness of the elastic elements on the natural frequencies and modes is examined

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

REFERENCES

  1. I. Ya. Amiro and V. A. Zarutskii, Statics, Dynamics, and Stability of Ribbed Shells [in Russian], Nauka, Moscow (1990).

    Google Scholar 

  2. L. M. Dmitrieva and Yu. P. Zhigalko, “Vibration of a rib-reinforced shallow cylindrical shell,” in: Research on the Theory of Plates and Shells [in Russian], Issue 14, Izd. Kazan. Univ., Kazan (1979), pp. 197–202.

    Google Scholar 

  3. Yu. P. Zhigalko, “Some problems of the dynamics of reinforced shells,” in: Research on the Theory of Plates and Shells [in Russian], Issue 14, Izd. Kazan. Univ., Kazan (1979), pp. 172–184.

    Google Scholar 

  4. V. A. Zarutskii, “The theory and methods of the stress-strain analysis of ribbed shells,” Int. Appl. Mech., 36, No.10, 1259–1283 (2000).

    Article  MATH  MathSciNet  Google Scholar 

  5. V. S. Karpilovskii, E. Z. Kriksunov, and S. Yu. Fialko, “Block Lanczos method with spectral transformations for large FEM problems of natural vibrations,” Visn. Odes. Nats. Morsk. Univ., No. 10, 93–99 (2003).

  6. V. S. Karpilovskii, E. Z. Kriksunov, A. V. Perel'muter, M. A. Perel'muter, and A. T. Trofimchuk, SCAD: User's Guide [in Russian], Kompas, Kiev (2000).

    Google Scholar 

  7. I. S. Malyutin and A. A. Bagdasaryan, “Free vibrations of an orthotropic cylindrical panel with glued ring ribs,” Mekh. Polim., No. 6, 35–42 (1976).

    Google Scholar 

  8. A. V. Perel'muter, V. S. Karpilovskii, K. V. Egupov, and S. Yu. Fialko, “Experience of implementing a draft of the International Building Regulations (MSN SNG) ‘Construction in Seismic Areas’ in the SCAD software system,” Visn. Odes. Derzh. Akad. Budivn. Arkhitekt., No. 9, 147–159 (2003).

  9. S. Yu. Fialko, “Features of the analysis of natural frequencies and modes in seismic design of structures,” Visn. Odes. Derzh. Akad. Budivn. Arkhitekt., No. 8, 193–201 (2002).

  10. S. Yu. Fialko, “Solving the generalized eigenvalue problem,” in: A. V. Perel'muter and V. I. Slivker (eds.), Design Models of Structures and Possibility for Their Analysis [in Russian], Kompas, Kiev (2002), pp. 570–597.

    Google Scholar 

  11. S. Yu. Fialko, “Modern computational techniques applied to multistory design,” Visn. Odes. Derzh. Akad. Budivn. Arkhitekt., No. 9, 189–193 (2003).

  12. S. Yu. Fialko, “Comparison of direct and iteration methods for solving large finite-element problems of structural mechanics,” in: A. V. Perel'muter and V. I. Slivker (eds.), Design Models of Structures and Possibility for Their Analysis [in Russian], Kompas, Kiev (2002), pp. 552–569.

    Google Scholar 

  13. S. Yu. Fialko and E. K. Ankyanets, “Modern computational techniques applied to natural vibrations of shells,” Zb. Nauk. Prats. Prydnipr. Derzh. Akad. Budivn. Arkhitekt. Varshav. Techn. Univ., No. 6, 835–842 (2004).

  14. K. J. Bathe, Finite Element Procedures, Prentice Hall, New Jersey (1996).

    Google Scholar 

  15. A. Ibrahimbegovic, R. L. Taylor, and E. L. Wilson, “A robust quadrilateral membrane finite element with drilling degrees of freedom,” Int. J. Numer. Meth. Eng., 30, 445–457 (1990).

    Article  Google Scholar 

  16. I. Katili, “A new discrete Kirchhoff-Mindlin element based on Mindlin-Reissner plate theory and assumed shear strain fields. Part II. An extended DKQ element for thick-plate bending analysis,” Int. J. Numer. Meth. Eng., 36, 1885–1908 (1993).

    MATH  Google Scholar 

  17. V. A. Zarutskii, “On the applicability domain of the assumptions in the theory of ribbed shells,” Int. Appl. Mech., 39, No.3, 307–311 (2003).

    Article  MATH  Google Scholar 

  18. V. A. Zarutskii and N. Ya. Prokopenko, “Dispersion equations for harmonic waves propagating along a cylindrical shell reinforced with a rib mesh (single-mode approximation),” Int. Appl. Mech., 40, No.2, 190–198 (2004).

    Article  Google Scholar 

  19. V. A. Zarutskii and N. Ya. Prokopenko, “Influence of discrete longitudinal ribs on harmonic waves in cylindrical shells,” Int. Appl. Mech., 39, No.4, 457–463 (2003).

    Article  Google Scholar 

  20. O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method. The Basis, Vol. 1, McGraw-Hill, New-York (2000).

    Google Scholar 

  21. O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method. Solid Mechanics, Vol. 2, McGraw-Hill, New-York (2000).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

__________

Translated from Prikladnaya Mekhanika, Vol. 41, No. 8, pp. 105–110, August 2005.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ankyanets, E.K. Natural Vibrations of a Cylindrical Shell Reinforced with Two-Layer Rings. Int Appl Mech 41, 924–928 (2005). https://doi.org/10.1007/s10778-005-0161-x

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10778-005-0161-x

Keywords

Navigation