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Research Papers

Free and Forced Vibration Analysis of Ring-Stiffened Conical–Cylindrical–Spherical Shells Through a Semi-Analytic Method

[+] Author and Article Information
Kun Xie

School of Naval Architecture
and Ocean Engineering,
Huazhong University of
Science and Technology,
1037 Luoyu Road,
Wuhan 430074, China
e-mail: xiekun79@163.com

Meixia Chen

School of Naval Architecture
and Ocean Engineering,
Huazhong University of
Science and Technology,
1037 Luoyu Road,
Wuhan 430074, China
e-mail: chenmx26@hust.edu.cn

Zuhui Li

School of Naval Architecture
and Ocean Engineering,
Huazhong University of
Science and Technology,
1037 Luoyu Road,
Wuhan 430074, China
e-mail: lizuhui925@hust.edu.cn

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received July 21, 2016; final manuscript received December 5, 2016; published online March 16, 2017. Assoc. Editor: Izhak Bucher.

J. Vib. Acoust 139(3), 031001 (Mar 16, 2017) (16 pages) Paper No: VIB-16-1358; doi: 10.1115/1.4035482 History: Received July 21, 2016; Revised December 05, 2016

A semi-analytic method is presented to analyze free and forced vibrations of combined conical–cylindrical–spherical shells with ring stiffeners and bulkheads. First, according to locations of discontinuity, the combined shell is divided into one opened spherical shell and a number of conical segments, cylindrical segments, stiffeners, and bulkheads. Meanwhile, a semi-analytic approach is proposed to analyze the opened spherical shell. The opened spherical shell is divided into narrow strips, which are approximately treated as conical shells. Then, Flügge theory is adopted to describe motions of conical and cylindrical segments, and stiffeners with rectangular cross section are modeled as annular plates. Displacement functions of conical segments, cylindrical segments, and annular plates are expanded as power series, wave functions, and Bessel functions, respectively. To analyze arbitrary boundary conditions, artificial springs are employed to restrain displacements at boundaries. Last, continuity and boundary conditions are synthesized to the final governing equation. In vibration characteristics analysis, high accuracy of the present method is first demonstrated by comparing results of the present method with ones in literature and calculated by ansys. Further, axial displacement of boundaries and open angle of spherical shell have significant influence on the first two modes, and forced vibrations are easily affected by bulkheads and external force.

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Figures

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Fig. 1

Schematic diagram of a combined conical–cylindrical–spherical shell and corresponding substructures: (a) combined shell (b) substructures

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Fig. 2

Schematic diagram of an opened spherical shell

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Fig. 3

Mode shapes of M1 with φ0 = 45 deg and Δφ0 = 0.5 deg

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Fig. 4

Mode shapes of M2 with F (Δφ0 = 0.5 deg)

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Fig. 5

Effects of stiffness constant on frequency parameters: (a) first mode and (b) second mode

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Fig. 6

Effects of boundary conditions on frequency parameters: (a) m = 1 and (b) m = 2

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Fig. 7

Effects of open angle φ0 on frequency parameters as φ1 = 90 deg: (a) C and (b) F

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Fig. 8

Effects of open angle φ1 on frequency parameters as φ0 = 0 deg: (a) C and (b) F

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Fig. 9

Effects of stiffeners on frequency parameters: (a) C and (b) F

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Fig. 10

Effects of bulkheads on frequency parameters: (a) C and (b) F

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Fig. 11

Effects of bulkheads on mode shapes

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Fig. 12

Effects of truncated circumferential mode number on frequency responses of driving point: (a) radial displacement and (b) axial displacement

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Fig. 13

Comparison of frequency responses of driving point of the present method and ansys: (a) radial displacement and (b) axial displacement

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Fig. 14

Contributions of different circumferential modes to frequency responses of driving point: (a) radial displacement and (b) axial displacement

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Fig. 15

Effects of bulkheads on frequency responses of driving point: (a) radial displacement and (b) axial displacement

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Fig. 16

Effects of external force on frequency responses of driving point: (a) radial displacement and (b) axial displacement

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Fig. 17

Effects of structural damping on frequency responsesof driving point: (a) radial displacement and (b) axial displacement

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