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Research Papers

Dynamic Analysis of Circular Cylindrical Shells With General Boundary Conditions Using Modified Fourier Series Method

[+] Author and Article Information
Lu Dai, Jingtao Du, Guoyong Jin

College of Power and Energy Engineering,  Harbin Engineering University, Harbin 150001, People’s Republic of China

Tiejun Yang1

College of Power and Energy Engineering,  Harbin Engineering University, Harbin 150001, People’s Republic of Chinayangtiejun@yahoo.cn

W. L. Li

Department of Mechanical Engineering,  Wayne State University, 5050 Anthony Wayne Drive, Detroit, MI 48202-3902

1

Corresponding author.

J. Vib. Acoust 134(4), 041004 (May 31, 2012) (12 pages) doi:10.1115/1.4005833 History: Received January 09, 2011; Revised September 27, 2011; Published May 29, 2012; Online May 31, 2012

Dynamic behavior of cylindrical shell structures is an important research topic since they have been extensively used in practical engineering applications. However, the dynamic analysis of circular cylindrical shells with general boundary conditions is rarely studied in the literature probably because of a lack of viable analytical or numerical techniques. In addition, the use of existing solution procedures, which are often only customized for a specific set of different boundary conditions, can easily be inundated by the variety of possible boundary conditions encountered in practice. For instance, even only considering the classical (homogeneous) boundary conditions, one will have a total of 136 different combinations. In this investigation, the flexural and in-plane displacements are generally sought, regardless of boundary conditions, as a simple Fourier series supplemented by several closed-form functions. As a result, a unified analytical method is generally developed for the vibration analysis of circular cylindrical shells with arbitrary boundary conditions including all the classical ones. The Rayleigh-Ritz method is employed to find the displacement solutions. Several examples are given to demonstrate the accuracy and convergence of the current solutions. The modal characteristics and vibration responses of elastically supported shells are discussed for various restraining stiffnesses and configurations. Although the stiffness distributions are here considered to be uniform along the circumferences, the current method can be readily extended to cylindrical shells with nonuniform elastic restraints.

Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Modeling of the shell and its boundary conditions

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Figure 2

Convergence of the frequency parameters Ω=ωRρ(1-μ2)/E for n = 1

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Figure 3

Convergence of the frequency parameters Ω=ωRρ(1-μ2)/E for n = 2

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Figure 4

Impact on the natural frequency of the stiffnesses of the elastic supports for some lower order modes

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Figure 5

Impact on the natural frequency of the stiffnesses of the elastic supports for some higher order modes

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Figure 6

Drive point mobilities for a simply supported shell

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Figure 7

Transfer point mobilities for a simply supported shell

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Figure 8

Drive point mobilities for a simply supported shell, due to a force excitation alone

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Figure 9

Transfer point mobilities for a simply supported shell, due to a force excitation alone

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Figure 10

Drive point mobilities for a clamped shell, due to a force excitation alone

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Figure 11

Transfer point mobilities for a clamped shell, due to a force excitation alone

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Figure 12

Drive point mobilities for different values of kr0

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Figure 13

Transfer point mobilities for different values of kr0

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Figure 14

Drive point mobilities for different values of kθ0

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Figure 15

Transfer point mobilities for different values of kθ0

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