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Vibration Analysis of Doubly Curved Shallow Shells With Elastic Edge Restraints

[+] Author and Article Information
Shiliang Jiang

College of Power and Energy 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 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 135(3), 034502 (Mar 28, 2013) (4 pages) Paper No: VIB-12-1318; doi: 10.1115/1.4023146 History: Received November 15, 2012; Revised November 20, 2012

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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Figures

Grahic Jump Location
Fig. 1

A doubly curved shallow shell with elastically restrained edges

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