Research Papers

Free Vibration of Moderately Thick Conical Shells Using a Higher Order Shear Deformable Theory

[+] Author and Article Information
R. D. Firouz-Abadi

Associate Professor
Department of Aerospace Engineering,
Sharif University of Technology,
Tehran 11155-8639, Iran
e-mail: Firouzabadi@sharif.edu

M. Rahmanian

Department of Aerospace Engineering,
Sharif University of Technology,
Tehran 11155-8639, Iran
e-mail: Rahmanian@ae.sharif.edu

M. Amabili

Department of Mechanical Engineering,
McGill University,
817 Sherbrooke Street West,
Montreal, PQ H3A 2K6, Canada
e-mail: marco.amabili@mcgill.ca

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received October 19, 2012; final manuscript received June 13, 2014; published online July 25, 2014. Assoc. Editor: Olivier A. Bauchau.

J. Vib. Acoust 136(5), 051001 (Jul 25, 2014) (8 pages) Paper No: VIB-12-1295; doi: 10.1115/1.4027862 History: Received October 19, 2012; Revised June 13, 2014

The present study considers the free vibration analysis of moderately thick conical shells based on the Novozhilov theory. The higher order governing equations of motion and the associate boundary conditions are obtained for the first time. Using the Frobenius method, exact base solutions are obtained in the form of power series via general recursive relations which can be applied for any arbitrary boundary conditions. The obtained results are compared with the literature and very good agreement (up to 4%) is achieved. A comprehensive parametric study is performed to provide an insight into the variation of the natural frequencies with respect to thickness, semivertex angle, circumferential wave numbers for clamped (C), and simply supported (SS) boundary conditions.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.


Lam, K., and Hua, L., 1999, “On Free Vibration of a Rotating Truncated Circular Orthotropic Conical Shell,” Composites Part B, 30(2), pp. 135–144. [CrossRef]
Civalek, O., 2006, “An Efficient Method for Free Vibration Analysis of Rotating Truncated Conical Shells,” Int. J. Press. Vessels Pip., 83(1), pp. 1–12. [CrossRef]
Hua, L., 2000, “Influence of Boundary Conditions on the Free Vibrations of Rotating Truncated Circular Multi-Layered Conical Shells,” Composites Part B, 31(4), pp. 265–275. [CrossRef]
Liu, M., Liu, J., and Cheng, Y. S., 2014, “Free Vibration of a Fluid Loaded Ring-Stiffened Conical Shell With Variable Thickness,” ASME J. Vib. Acoust. (in press). [CrossRef]
Wang, Y., Liu, R., and Wang, X., 1999, “Free Vibration Analysis of Truncated Conical Shells by the Differential Quadrature Method,” Int. J. Sound Vib., 224(2), pp. 387–394. [CrossRef]
Qu, Y., Chen, Y., Chen, Y., Long, X., Hua, H., and Meng, G., 2013, “A Domain Decomposition Method for Vibration Analysis of Conical Shells With Uniform and Stepped Thickness,” ASME J. Vib. Acoust., 135(1), p. 011014. [CrossRef]
Lakis, A., Dyke, P. V., and Ouriche, H., 1992, “Dynamic Analysis of Anisotropic Fluid-Filled Conical Shells,” J. Fluids Struct., 6(2), pp. 135–162. [CrossRef]
Sabri, F., and Lakis, A., 2010, “Hybrid Finite Element Method Applied to Supersonic Flutter of an Empty or Partially Liquid-Filled Truncated Conical Shell,” J. Sound Vib., 329(3), pp. 302–316. [CrossRef]
Liew, K. M., Ng, T. Y., and Zhao, X., 2005, “Free Vibration Analysis of Conical Shells Via the Element-Free kp-Ritz Method,” J. Sound Vib., 281(35), pp. 627–645. [CrossRef]
Amabili, M., 2008, Nonlinear Vibrations and Stability of Shells and Plates, Cambridge University, New York.
Leissa, A. W., 1973, “Vibration of Shells,” National Aeronautics and Space Administration, Washington, DC, Paper No. NASA SP-288.
Kayran, A., and Vinson, J. R., 1990, “Free Vibration Analysis of Laminated Composite Truncated Circular Conical Shells,” AIAA J., 28(7), pp. 1259–1269. [CrossRef]
Valathur, M., and Albrecht, B., 1971, “On Axisymmetric Free Vibrations of Thin Truncated Conical Shells,” J. Sound Vib., 18(1), pp. 9–16. [CrossRef]
Tong, L., 1993, “Free Vibration of Orthotropic Conical Shells,” Int. J. Eng. Sci., 31(5), pp. 719–733. [CrossRef]
Tong, L., 1993, “Free Vibration of Composite Laminated Conical Shells,” Int. J. Mech. Sci., 35(1), pp. 47–61. [CrossRef]
Tong, L., 1994, “Free Vibration of Laminated Conical Shells Including Transverse Shear Deformation,” Int. J. Solids Struct., 31(4), pp. 443–456. [CrossRef]
Amabili, M., and Reddy, J., 2010, “A New Non-Linear Higher-Order Shear Deformation Theory for Large-Amplitude Vibrations of Laminated Doubly Curved Shells,” Int. J. Non Linear Mech., 45(4), pp. 409–418. [CrossRef]
Amabili, M., 2012, “A New Nonlinear Higher-Order Shear Deformation Theory With Thickness Variation for Large-Amplitude Vibrations of Laminated Doubly Curved Shells,” J. Sound Vib., 332(19), pp. 4620–4640. [CrossRef]
Novozhilov, V. V., 1999, Foundations of the Nonlinear Theory of Elasticity, Courier Dover Publications, Mineola, NY.
Irie, T., Yamada, G., and Tanaka, K., 1984, “Natural Frequencies of Truncated Conical Shells,” J. Sound Vib., 92(3), pp. 447–453. [CrossRef]
Loy, C., and Lam, K., 1999, “Vibration of Thick Cylindrical Shells on the Basis of Three-Dimensional Theory of Elasticity,” J. Sound Vib., 226(4), pp. 719–737. [CrossRef]


Grahic Jump Location
Fig. 1

Geometry of the truncated conical shell

Grahic Jump Location
Fig. 2

Semivertex angle effect on the frequency parameter for the C–C and S–S boundary conditions: (a) n = 0, (b) n = 1, and (c) n = 2

Grahic Jump Location
Fig. 3

Thickness ratio effect on the frequency parameter for the C–C and S–S boundary conditions: (a) n = 0, (b) n = 1, and (c) n = 2

Grahic Jump Location
Fig. 4

The frequency parameter variations versus the circumferential half-wave number for the C–C and S–S boundary conditions: (a) m = 1 and (b) m = 2




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In