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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

Professor
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.

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Figures

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Fig. 1

Geometry of the truncated conical shell

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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

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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

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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

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