A method for determining the natural frequencies of compound shells of revolution with a branched meridian is proposed. This method combines the Fourier method, the incremental search method (∆(λ)-method), and the orthogonal-sweep method. The method is tested against specific examples. The dependence of the lower frequencies of a cylinder–ring-plate system on the relative stiffness of its components is studied.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
M. S. Ganeeva and Z. V. Skvortsova, “Equations of the free vibrations and neutral equilibrium of nonthin shells of revolution with branched meridian under axisymmetric thermomechanical loading,” in: Important Problems in Continuum Mechanics [in Russian], Izd. KGU, Kazan (2006), pp. 199–209.
Ya. M. Grigorenko, V. I. Gololobov, L. D. Krivoruchko, N. A. Lobkova, and V. V. Semenova, ”Stress design of branched shells of revolution,” Prikl. Mech., 20, No. 7, 101–104 (1984).
Ya. M. Grigorenko, E. I. Bespalova, A. B. Kitaigorodskii, and A. I. Shinkar’, Free Vibrations of Elements of Shell Structures [in Russian], Naukova Dumka, Kyiv (1986).
V. I. Gulyaev and I. L. Solov’ev, “Precessional vibrations and resonances of compound shells during complex rotation,” Int. Appl. Mech., 35, No. 6, 602–609 (1999).
Yu. V. Klochkov, A. P. Nikolaev, S. S. Marchenko, and A. A. Shubovich, “Analysis of a shell of revolution with branched meridian using a quadrilateral finite element and various interpolations of the displacement fields,” Izv. VUZov, Storit., No. 5, 3–13 (2011).
E. I. Bespalova and G. P. Urusova, “Stress state of branched shells of revolution subject to transverse shear and reduction,” Int. Appl. Mech., 51, No. 4, 410–419 (2015).
E. Bespalova and G. Urusova, “Vibration of highly inhomogeneous shells of revolution under static loading,” J. Mech. Mater. Struct., 3, No. 7, 1299–1313 (2008).
A. Benjeddou, “Vibrations of complex shells of revolution using B-spline finite elements,” Comput. Struct., 74, No. 4, 429–440 (2000).
D. Bushnell, “Stress, stability and vibration of complex, branched shells of revolution,” Comput. Struct., 4, 339–435 (1974).
M. Caresta and N. J. Kessissoglou, “Free vibrational characteristics of isotropic coupled cylindrical–conical shells,” J. Sound Vibr., 329, No. 6, 733–751 (2010).
D. Chronopoulos, M. Ichchou, B. Troclet, and O. Bareille, “Predicting the broadband response of a layered cone-cylinder-cone shell,” Comp. Struct., 107, 149–159 (2014).
G. Cohen, “FASOR—a program for stress, buckling and vibration of shells of revolution,” Adv. Eng. Software, 3, No. 4, 155–162 (1981).
S. B. Filippov and N. V. Naumova, “Axisymmetric vibrations of thin shells of revolution joint by a small angle,” Technische Mechanik, 18, No. 4, 285–291 (1998).
A. Z. Galishin, V. A. Merzlyakov, and Yu. N. Shevchenko, “Application of the Newton method for calculating the axisymmetric thermoelastoplastic state of flexible laminar branched shells using the shear model,” Mech. Comp. Mater., 37, No. 3, 189–200 (2001).
Ya. M. Grigorenko and A. Ya. Grigorenko, “Static and dynamic problems for anisotropic inhomogeneous shells with variable parameters and their numerical solution (review),” Int. Appl. Mech., 49, No. 2, 123–193 (2013).
W. C. L. Hu and J. P. Raney, “Experimental and analytical study of vibrations of joined shells,” AIAA J., 5, No. 5, 976–980 (1967).
A. Kayran and E. Yavuzbalkan, “Free-vibration analysis of ring-stiffened branched composite shells of revolution,” AIAA J., 48, No. 4, 749–762 (2010).
Y. S. Lee, M. S. Yang, Y. S. Kim, and J. H. Kim, “A study on the free vibration of the joined cylindrical–spherical shell structures,” Comput. Struct., 80, 2405–2414 (2002).
V. A. Maximyuk, E. A. Storozhuk, and I. S. Chernyshenko, “Variational finite-difference methods in linear and nonlinear problems of the deformation of metallic and composite shells (review),” Int. Appl. Mech., 48, No. 6, 613–687 (2012).
B. P. Patel, M. Ganapathi, and S. Kamat, “Free vibration characteristics of laminated composite joined conical-cylindrical shells,” J. Sound Vibr., 237, No. 5, 920–930 (2000).
Y. Qu, S. Wu, Y. Chen, and H. Hua, “Vibration analysis of ring-stiffened conical–cylindrical–spherical shells based on a modified variational approach,” Int. J. Mech. Sci., 69, 72–84 (2013).
S. Wu, Y. Qu, and H. Hua, “Vibration characteristics of a spherical–cylindrical–spherical shell by a domain decomposition method,” Mech. Res. Commun., 49, 17–26 (2013).
A. Zolochevsky, A. Galishin, S. Sklepus, and G. Z. Voyiadjis, “Analysis of creep deformation and creep damage in thin-walled branched shells from materials with different behavior in tension and compression,” Int. J. Solids Struct., 44, 5075–5100 (2007).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Prikladnaya Mekhanika, Vol. 52, No. 1, pp. 117–126, January–February, 2016.
Rights and permissions
About this article
Cite this article
Bespalova, E.I., Urusova, G.P. Vibrations of Shells of Revolution with Branched Meridian. Int Appl Mech 52, 82–89 (2016). https://doi.org/10.1007/s10778-016-0735-9
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10778-016-0735-9