Technical Brief

Bryan's Factor for Truncated Spherical and Conical Shells

[+] Author and Article Information
K. Y. Narasimhan

Lockheed Martin Space Systems,
Sunnyvale, CA 94088-3504
e-mail: k.y.narasimhan@gmail.com

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received September 8, 2013; final manuscript received January 29, 2014; published online March 18, 2014. Assoc. Editor: Jeffrey F. Rhoads.

J. Vib. Acoust 136(3), 034502 (Mar 18, 2014) (5 pages) Paper No: VIB-13-1312; doi: 10.1115/1.4026674 History: Received September 08, 2013; Revised January 29, 2014

Closed-form expressions are derived for the Bryan's factor of truncated spherical and conical shells through a Galerkin procedure. Results lead to the value obtained by G. H. Bryan for the case of the ring, thereby demonstrating accuracy of the method. It is shown that the Bryan's factor depends only on the shape of the structure and the modes of vibration. The material properties are required to determine the resonating frequency and the Q-factor.

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Fig. 1

The spherical coordinate system

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Fig. 2

Microscale HRG made of polycrystalline diamond

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Fig. 3

Truncated spherical shell parameters

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Fig. 4

Bryan's factor for truncated spherical shell

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Fig. 5

Coordinate system for truncated conical shell

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Fig. 6

Truncated conical shell parameters

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Fig. 7

BF for truncated conical shell for varying α between 0 degree and 180 degrees



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