An analytical method is derived for the vibration analysis of doubly curved shallow shells with arbitrary elastic supports alone its edges, a class of problems which are rarely attempted in the literature. Under this framework, all the classical homogeneous boundary conditions for both in-plane and out-of-plane displacements can be universally treated as the special cases when the stiffness for each of restraining springs is equal to either zero or infinity. Regardless of the boundary conditions, the displacement functions are invariably expanded as an improved trigonometric series which converges uniformly and polynomially over the entire solution domain. All the unknown expansion coefficients are treated as the generalized coordinates and solved using the Rayleigh–Ritz technique. Unlike most of the existing solution techniques, the current method offers a unified solution to a wide spectrum of shell problems involving, such as different boundary conditions, varying material and geometric properties with no need of modifying or adapting the solution schemes and implementing procedures. A numerical example is presented to demonstrate the accuracy and reliability of the current method.
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June 2013
Technical Briefs
Vibration Analysis of Doubly Curved Shallow Shells With Elastic Edge Restraints
Shiliang Jiang,
Shiliang Jiang
College of Power and Energy Engineering,
Department of Mechanical Engineering,
Harbin Engineering University
,Harbin, 150001
, People's Republic of China
;Department of Mechanical Engineering,
Wayne State University
,5050 Anthony Wayne Drive
,Detroit, MI 48202
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Tiejun Yang,
Tiejun Yang
1
College of Power and Energy Engineering,
Harbin, 150001,
e-mail: yangtiejun@yahoo.cn
Harbin Engineering University
,Harbin, 150001,
People's Republic of China
e-mail: yangtiejun@yahoo.cn
1Corresponding author.
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W. L. Li,
W. L. Li
Department of Mechanical Engineering,
Wayne State University
,5050 Anthony Wayne Drive
,Detroit, MI 48202
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Jingtao Du
Jingtao Du
College of Power and Energy Engineering,
Harbin Engineering University
,Harbin, 150001
, People's Republic of China
Search for other works by this author on:
Shiliang Jiang
College of Power and Energy Engineering,
Department of Mechanical Engineering,
Harbin Engineering University
,Harbin, 150001
, People's Republic of China
;Department of Mechanical Engineering,
Wayne State University
,5050 Anthony Wayne Drive
,Detroit, MI 48202
Tiejun Yang
College of Power and Energy Engineering,
Harbin, 150001,
e-mail: yangtiejun@yahoo.cn
Harbin Engineering University
,Harbin, 150001,
People's Republic of China
e-mail: yangtiejun@yahoo.cn
W. L. Li
Department of Mechanical Engineering,
Wayne State University
,5050 Anthony Wayne Drive
,Detroit, MI 48202
Jingtao Du
College of Power and Energy Engineering,
Harbin Engineering University
,Harbin, 150001
, People's Republic of China
1Corresponding author.
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received November 15, 2012; final manuscript received November 20, 2012; published online March 28, 2013. Assoc. Editor: Marco Amabili.
J. Vib. Acoust. Jun 2013, 135(3): 034502 (4 pages)
Published Online: March 28, 2013
Article history
Received:
November 15, 2012
Revision Received:
November 20, 2012
Citation
Jiang, S., Yang, T., Li, W. L., and Du, J. (March 28, 2013). "Vibration Analysis of Doubly Curved Shallow Shells With Elastic Edge Restraints." ASME. J. Vib. Acoust. June 2013; 135(3): 034502. https://doi.org/10.1115/1.4023146
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