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Research Papers

Wave Based Method for Free Vibration Analysis of Cylindrical Shells With Nonuniform Stiffener Distribution

[+] Author and Article Information
Meixia Chen

e-mail: chemx26@hust.edu.cn

Naiqi Deng

School of Naval Architecture
and Ocean Engineering,
Huazhong University of
Science and Technology,
Wuhan 430074, China

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the Journal of Vibration and Acoustics. Manuscript received December 11, 2012; final manuscript received February 25, 2013; published online June 19, 2013. Assoc. Editor: Marco Amabili.

J. Vib. Acoust 135(6), 061011 (Jun 19, 2013) (13 pages) Paper No: VIB-12-1345; doi: 10.1115/1.4024055 History: Received December 11, 2012; Revised February 25, 2013

Wave based method (WBM) is presented to analysis the free vibration characteristics of cylindrical shells with nonuniform stiffener distributions for arbitrary boundary conditions. The stiffeners are treated as discrete elements. The equations of motion of annular circular plate are used to describe the motion of stiffeners. Instead of expanding the dynamic field variables in terms of polynomial approximation in element based method (finite element method etc), the ring-stiffened cylindrical shell is divided into several substructures and the dynamic field variables in each substructure are expressed as wave function expansions. Boundary conditions and continuity conditions between adjacent substructures are used to form the final matrix to be solved. Natural frequencies of cylindrical shells with uniform rings spacing and eccentricity distributions for shear diaphragm-shear diaphragm boundary conditions have been calculated by WBM model which shows good agreement with the experimental results and the analytical results of other researchers. Natural frequencies of cylindrical shells with other boundary conditions have also been calculated and the results are compared with the finite element method which also shows good agreement. Effects of the nonuniform rings spacing and nonuniform eccentricity and effects of boundary conditions on the fundamental frequencies and the beam mode frequencies have been studied. Different stiffener distributions are needed to increase the fundamental frequencies and beam mode frequencies for different boundary conditions. WBM model presented in this paper can be recognized as a semianalytical and seminumerical method which is quite useful in analyzing the vibration characteristics of cylindrical shells with nonuniform rings spacing and eccentricity distributions.

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References

Figures

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Fig. 1

Ring stiffened cylindrical shells

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Fig. 2

Displacement of annular circular plate

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Fig. 3

Displacement constraints and force constraints

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Fig. 4

Interaction forces between stiffener and adjacent bays of cylindrical shells

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Fig. 5

Uniform and nonuniform rings spacing and eccentricity distribution

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Fig. 6

Natural frequency variations versus the depth of the first stiffener of equally rings spacing (d1 = 0.00314) and nonuniformly eccentricity distribution with SD-SD, SD-F, F-F boundary conditions: (a) SD-SD (b) F-F (c) SD-F —▪— n = 1 —•— n = 2 —▴— n = 3 —▾— n = 4 —◂— n = 5 —▸— n = 6

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Fig. 7

Fundamental frequency variations versus the depth of the first stiffener for given d1 with SD-SD, F-F, SD-F boundary conditions: (a) SD-SD (b) F-F (c) SD-F —▪— d1 = 0.0114 —•— d1 = 0.0164 —▴— d1 = 0.0214 —▾— d1 = 0.0264 —◂— d1 = 0.0314 —▸— d1 = 0.0364 —♦— d1 = 0.0414 —★— d1 = 0.0464 —◊— d1 = 0.0514

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Fig. 8

Beam mode frequency variations versus the depth of the first stiffener for given d1 with SD-SD, F-F, SD-F boundary conditions: (a) SD-SD (b) F-F (c) SD-F —▪— d1 = 0.0114 —•— d1 = 0.0164 —▴— d1 = 0.0214 —▾— d1 = 0.0264 —◂— d1 = 0.0314 —▸— d1 = 0.0364 —♦— d1 = 0.0414 —★— d1 = 0.0464 —◊— d1 = 0.0514

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