Abstract
The system of equations and its numerical solution for free and forced oscillations of shells of revolution with an arbitrary meridian is obtained. A variant of the classical theory of shells developed on the basis of Lagrangian mechanics is used. The natural frequencies and amplitudes of oscillations of shells with various meridians are defined by the finite difference method.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Berdichevsky VL (2009) Variational principles of continuum mechanics. V.2. Applications. Springer, Berlin, p 1014. doi:10.1007/978-3-540-88469-9
Birger IA (1992) Rods, plates, shells (Sterzhni, plastinki, obolochki). Nauka, Moscow, p 392 (in Russian)
Blaauwendraad J, Hoefakker JH (2014) Structural shell analysis. Springer, The Netherlands, p 300. doi:10.1007/978-94-007-6701-0
Chapelle D, Bathe KJ (2011) The finite element analysis of shells—fundamentals, computational fluid and solid mechanics, 2nd edn. Springer, Berlin, p 410. doi:10.1007/978-3-642-16408-8
Donnell LG (1982) Beams, plates and shells (Balki, plastiny i obolochki). Nauka, Moscow, p 568 (in Russian)
Eremeev VA, Zubov LM (2008) Mechanics of elastic shells (Mekhanika uprugih obolochek). Nauka, Moscow, p 280 (in Russian)
Goldenvejzer AL (1976) Theory of elastic thin shells (Teoriya uprugih tonkih obolochek). Nauka, Moscow, p 512 (in Russian)
Khanh CL (1999) Vibrations of shells and rods. Springer, Berlin, p 423. doi:10.1007/978-3-642-59911-8
Novozhilov VV, Chernykh KF, Mikhajlovskij EM (1991) Linear theory of thin shells (Linejnaya teoriya tonkih obolochek). Politekhnika, Leningrad, p 656 (in Russian)
Eliseev VV (2003) Mechanics of elastic bodies (Mekhanika uprugih tel). St. Petersburg State Polytechnic University Publishing House, St Petersburg, p 336 (in Russian)
Eliseev VV (2006) To nonlinear theory of elastic shells (K nelineynoy teorii uprugih obolochek) St. Petersburg State Polytechnic University Journal (Nauchno-tekhnicheskie vedomosti SPbGTU). No. 3, pp 35–39 (in Russian)
Eliseev VV, Vetyukov YM (2010) Finite deformation of thin shells in the context of analytical mechanics of material surfaces. Acta Mech 209:43–57. doi:10.1007/s00707-009-0154-7
Eliseev VV, Vetyukov YM (2014) Theory of shells as a product of analytical technologies in elastic body mechanics. Shell Struct Theor Appl 3:81–85
Filippenko GV (2016) The vibrations of reservoirs and cylindrical supports of hydro technical constructions partially submerged into the liquid. In: Evgrafov A (ed) Advances in mechanical engineering, lecture notes in mechanical engineering. Springer International Publishing, Switzerland, pp 115–126
Eliseev VV, Vetyukov YM, Zinov’eva TV (2011) Divergence of a helicoidal shell in a pipe with a flowing fluid. J Appl Mech Tech Phys 52:450–458. doi:10.1134/S0021894411030151
Yeliseyev VV, Zinovieva TV (2014) Two-dimensional (shell-type) and three-dimensional models for elastic thin-walled cylinder. PNRPU Mech Bull 3:50–70. doi:10.15593/perm.mech/2014.3.04
Zinovieva TV (2012) Computational mechanics of elastic shells of revolution in mechanical engineering calculations. In: Modern engineering: science and education. Proceedings of second international scientific and practical conference. State Polytechnic University, St. Petersburg, pp 335–343
Bakhvalov NS, Zhidkov NP, Kobelkov GG (2011) Numerical methods (Chislennye metody) Binom. Laboratory of knowledge, Moscow, p 640 (In Russian)
Borwein JM, Skerritt MB (2012) An introduction to modern mathematical computing: with Mathematica, vol XVI. Springer, p 224
Chapra SC, Canale RP (2014) Numerical methods for engineers. McGraw-Hill Education, New York, p 992
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Zinovieva, T.V. (2017). Calculation of Shells of Revolution with Arbitrary Meridian Oscillations. In: Evgrafov, A. (eds) Advances in Mechanical Engineering. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-53363-6_17
Download citation
DOI: https://doi.org/10.1007/978-3-319-53363-6_17
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-53362-9
Online ISBN: 978-3-319-53363-6
eBook Packages: EngineeringEngineering (R0)