Dynamic analysis of FG stepped truncated conical shells surrounded by Pasternak elastic foundations

Le Quang Vinh, Nguyen Manh Cuong


This research presents a continuous element model for solving vibration problems of FG stepped truncated conical shells having various material properties and surrounded by Pasternak foundations. Based on the First Order Shear Deformation Theory (FSDT) and the equations of the FGM conical shells, the dynamic stiffness matrix is obtained for each segment of the shell having constant thickness. The interesting assembly procedure of continuous element method (CEM) is employed for joining those segments in order to analyze the dynamic behavior of the FG stepped truncated conical shells an assembly procedure of continuous element method (CEM) is employed for joining those segments. Free vibrations of different configurations of FG stepped truncated conical shells on elastic foundations are examined. Effects of structural parameters, stepped thickness and elastic foundations on the free vibration of FG stepped truncated conical shells are also presented.


stepped shell; vibration of conical shell; functionally graded shell; continuous element method; Winkler–Pasternak foundation

Full Text:



P. L. Pasternak. On a new method of analysis of an elastic foundation by means of two foundation constants. Gos. Izd. Lit. po Stroit I Arkh. Moscow, USSR, (1954). (in Russian).

A. D. Kerr. Elastic and viscoelastic foundation models. Journal of Applied Mechanics, 31, (1964), pp. 491–498. https://doi.org/10.1115/1.3629667.

A. H. Sofiyev and N. Kuruoglu. Vibration analysis of FGM truncated and complete conical shells resting on elastic foundations under various boundary conditions. Journal of Engineering Mathematics, 77, (1), (2012), pp. 131–145. https://doi.org/10.1007/s10665-012-9535-3.

A. H. Sofiyev and E. Schnack. The vibration analysis of FGM truncated conical shells resting on two-parameter elastic foundations. Mechanics of Advanced Materials and Structures, 19, (4), (2012), pp. 241–249. https://doi.org/10.1080/15376494.2011.642934.

H. L. K. Dung, Dao Van and N. T. Nga. On the stability of functionally graded truncated conical shells reinforced by functionally graded stiffeners and surrounded by an elastic medium. Composite Structures, 108, (2014), pp. 77–90. https://doi.org/10.1016/j.compstruct.2013.09.002.

K. Xie, M. Chen, and Z. Li. An analytic method for free and forced vibration analysis of stepped conical shells with arbitrary boundary conditions. Thin-Walled Structures, 111, (2017), pp. 126–137. https://doi.org/10.1016/j.tws.2016.11.017.

Y. Qu, Y. Chen, Y. Chen, X. Long, H. Hua, and G. Meng. A domain decomposition method for vibration analysis of conical shells with uniform and stepped thickness. Journal of Vibration and Acoustics, 135, (1), (2013). https://doi.org/10.1115/1.4006753.

L. Q. Vinh, N. M. Cuong, and L. T. B. Nam. Dynamic analysis of stepped composite conical shells via continuous element method. In 2nd National Conference on Mechanical Engineering and Automation, Hanoi, Vietnam, (2016), pp. 338–344.

L. T. B. Nam, N. M. Cuong, T. I. Tran, and L. Q. Vinh. Dynamic analysis of stepped composite cylindrical shells surrounded by Pasternak elastic foundations based on the continuous element method. Vietnam Journal of Mechanics, 40, (2), (2018), pp. 105–119. https://doi.org/10.15625/0866-7136/9832.

DOI: https://doi.org/10.15625/0866-7136/14749 Display counter: Abstract : 200 views. PDF : 51 views.


  • There are currently no refbacks.

Copyright (c) 2020 Vietnam Academy of Science and Technology


Editorial Office of Vietnam Journal of Mechanics

3rd Floor, A16 Building, 18B Hoang Quoc Viet Street, Cau Giay District, Hanoi, Vietnam
Tel: (+84) 24 3791 7103
Email: vjmech@vjs.ac.vn