Research Papers

Free Vibration of Doubly Curved Thin Shells

[+] Author and Article Information
April Bryan

No. 7 Jack Trace, Enterprise,
Chaguanas 500234, Trinidad and Tobago
e-mail: aprilbr@gmail.com

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received August 12, 2017; final manuscript received November 3, 2017; published online December 20, 2017. Assoc. Editor: Stefano Lenci.

J. Vib. Acoust 140(3), 031003 (Dec 20, 2017) (11 pages) Paper No: VIB-17-1366; doi: 10.1115/1.4038578 History: Received August 12, 2017; Revised November 03, 2017

While several numerical approaches exist for the vibration analysis of thin shells, there is a lack of analytical approaches to address this problem. This is due to complications that arise from coupling between the midsurface and normal coordinates in the transverse differential equation of motion (TDEM) of the shell. In this research, an Uncoupling Theorem for solving the TDEM of doubly curved, thin shells with equivalent radii is introduced. The use of the uncoupling theorem leads to the development of an uncoupled transverse differential of motion for the shells under consideration. Solution of the uncoupled spatial equation results in a general expression for the eigenfrequencies of these shells. The theorem is applied to four shell geometries, and numerical examples are used to demonstrate the influence of material and geometric parameters on the eigenfrequencies of these shells.

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Fig. 1

Geometry of the doubly curved thin shell

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Fig. 2

Stresses acting on a single element of a doubly curved thin shell

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Fig. 3

Geometry of the SC

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Fig. 4

Geometry of the RC

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Fig. 5

Geometry of the EC

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Fig. 6

Geometry of the SS

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Fig. 7

First ten eigenfrequencies for the SC, RC, EC, and SS

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Fig. 8

The effect of radius and thickness on ω for the first and tenth modes: (a) SC, (b) RC, (c) EC, and (d) SS

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Fig. 9

ω′/ω versus radii and thickness for the first and tenth modes: (a) SC, (b) RC, (c) EC, and (d) SS

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Fig. 10

Effect of aspect ratio on ω



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