The dynamics of asymmetric three-layer spherical shells with a ribbed discrete-symmetric lightweight core under nonstationary loading is studied. The elements of the elastic structure are analyzed using the Timoshenko model of the theory of shells and rods and independent static and kinematic hypotheses for each layer. The equations of motion of the shells under axisymmetric impulsive loading are derived using the Hamilton–Ostrogradsky variational principle. A finite-element shell model that relates the potential strain energy in the body and the potential of the applied forces is developed. The numerical results on the dynamics of the asymmetric three-layer elastic structure with face layers made of dissimilar materials are obtained using the finite-element method. The effect of the geometrical and mechanical parameters of the asymmetric layers of the shell on its dynamic behavior under axisymmetric internal nonstationary loading is studied. New mechanical effects are revealed.
Similar content being viewed by others
References
S. A. Lychev and Yu. N. Saifutdinov, “Dynamics of three-layer nonshallow spherical shell,” Mekh. Predel’n. Sost., Vestnik ChGPU im. Yakovleva, No. 2, 54–90 (2007).
S. A. Lychev and Yu. A.Sidorov, “Nonstationary vibrations of three-layer spherical shells with a multiple spectrum,” Izv. Vuzov. Stroitel’stvo, No. 4, 31–39 (2001).
S. P. Orlenko, “Numerical modeling of the dynamics of a three-layer spherical shell with a discrete inhomogeneous core,” Dop. NAN Ukrainy, No. 3, 19–27 (2020).
S. P. Rychkov, Structural Modeling in Femap with NX Nastran [in Russian], DMK Press, Moscow (2013).
S. P. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells, McGraw-Hill, New York (1959).
V. G. Piskunov and A. O. Rasskazov, “Development of the theory of layered plates and shells,” in: Vol. 3 of the six-volume series Advances in Mechanics [in Russian], A.S.K., Kyiv (2007), pp. 141–175.
Y. Frostig and O. T. Thomsen, “Higher-order free vibration of sandwich panels with a flexible core,” Int. J. Solids Struct., 41, 1697–1724 (2004).
T. Hause and L. Librescu, “Postbuckling of anisotropic flat and doubly-curved sandwich panels under complex loading conditions,” Int. J. Solids Struct., 35, No. 23, 3007–3027 (1998).
T. Hause and L. Librescu, “Dynamic response of doubly-curved anisotropic sandwich panels impacted by blast loadings,” Int. J. Solids Struct., 44, No. 20, 6678–6700 (2007).
J. Hohe and L. Librescu, “Nonlinear theory for doubly-curved anisotropic sandwich shells with cross-compressed cores,” Int. J. Solids Struct., 40, No. 5, 1059–1088 (2003).
M. M. Kheirikhah, S. M. R. Khalili, and K. Malekzadeh Fard, “Biaxial buckling analyses of soft-core composite sandwich plates using improved high-order theory,” European J. Mech. A/Solids, 31, 54–66 (2011).
P. Z. Lugovoi and V. F. Meish, “Dynamics of inhomogeneous shell systems under nonstationary loading (Survey),” Int. Appl. Mech., 53, No. 5, 481–537 (2017).
P. Z. Lugovoi, V. F. Meish, Yu. A. Meish, and S. P. Orlenko, “Dynamic design of compound shell structures of revolution under nonstationary loads,” Int. Appl. Mech., 56, No. 1, 22–32 (2020).
P. Z. Lugovoi, V. F. Meish, and S. P. Orlenko, “Numerical simulation of the dynamics of spherical sandwich shells reinforced with discrete ribs under a shockwave,” Int. Appl. Mech., 56, No. 5, 590–598 (2020).
P. Z. Lugovoi, V. V. Gaidaichuk, Yu. V. Skosarenko, and K. E. Kotenko, “Stress–strain state of three-layer cylindrical shells with reinforced light core under nonstationary loading,” Int. Appl. Mech., 57, No. 4, 395–404 (2021).
P. Z. Lugovoi and S. P. Orlenko, “Effect of the asymmetry of cylindrical sandwich shells on their stress–strain state under nonstationary loading,” Int. Appl. Mech., 57, No. 5, 543–553 (2021).
K. Malekzadeh Fard, M. Livani, A. Veisi, and M. Gholami, “Improved high-order bending analysis of double curved sandwich panels subjected to multiple loading conditions,” Latin American J. Solids Struct., 11, 1591–1614 (2014).
V. F. Meish and S. E. Shtantsel, “Dynamic problems in the theory of sandwich shells of revolution with a discrete core under nonstationary loads,” Int. Appl. Mech., 38, No. 12, 1501–1507 (2002).
W. Muller, Ya. M. Grigorenko, A. Ya. Grigorenko, and G. G. Vlaikov, “Mechanics of Anisotropic Heterogeneous Shells: Fundamental Relations for Different Models.” From the book Recent Developments in Anisotropic Heterogenous Shell Theory: General Theory and Applications of Classical Theory, Vol. 1 (electronic resource), Springer, Singapure (2016).
M. S. Gatu, Vibration of Laminated Shells and Plates, Academic Press, New York (2004).
M. S. Gatu, R. W. Sullivan, and W. Wang, “Recent research advances in the dynamic behavior of composite shells,” Compos. Struct., 93, No. 1, 14–31 (2010).
J. N. Reddy, Mechanics of Laminated Composite Plates and Shells. Theory and Application, CRC Press, Boca Raton (2003).
N. A. Shhul’ga and V. F. Meish, “Forced vibration of three-layered spherical and ellipsoidal shells under axisymmetric loads,” Mech. Comp. Mater., 39, No. 5, 439–446 (2003).
M. Surianinov, T. Yemelianova, and O. Shyliaiev, “Investigation of free vibrations of three-layered circular shell supported by annular ribs of rigidity,” Materials Sci. Forum Actual Problems of Eng. Mech., 968, 437–443 (2019).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Prykladna Mekhanika, Vol. 59, No. 2, pp. 54–66, March–April 2023
This study was sponsored by the budgetary program Support of Priority Areas of Research (KPKVK 6541230).
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Lugovyi, P.Z., Gaidaichuk, V.V., Orlenko, S.P. et al. Dynamics of Asymmetric Three-Layer Spherical Shells with a Discretely Inhomogeneous Core Under Nonstationary Loading*. Int Appl Mech 59, 175–186 (2023). https://doi.org/10.1007/s10778-023-01211-3
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10778-023-01211-3