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Research Papers

Dynamic Analysis of General Rotationally Symmetric Built-Up Structures Using a Modified Fourier Spectral Element Approach

[+] Author and Article Information
Guoyong Jin

College of Power and Energy Engineering,
Harbin Engineering University,
Harbin 150001, China
e-mail: guoyongjin@hrbeu.edu.cn

Xianglong Ma, Zhigang Liu

College of Power and Energy Engineering,
Harbin Engineering University,
Harbin 150001, China

Lingkuang Xuan

National Key Laboratory on
Ship Vibration and Noise,
China Ship Development and Design Center,
Wuhan 430064, China

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received August 20, 2016; final manuscript received November 8, 2016; published online February 17, 2017. Assoc. Editor: Matthew Brake.

J. Vib. Acoust 139(2), 021012 (Feb 17, 2017) (13 pages) Paper No: VIB-16-1407; doi: 10.1115/1.4035226 History: Received August 20, 2016; Revised November 08, 2016

A modified Fourier spectral element method (SEM) is developed to study vibration behaviors of general built-up systems that consist of various rotationally symmetric structures, including conical, cylindrical, and spherical shells, and annular plates. The substructures are formulated as spectral elements based on the type of elementary structure. These spectral elements can be easily assembled using three-dimensional elastic couplers at the interfaces to coordinate the forces and moments of adjacent substructures with respect to a cylindrical coordinate system. A modified Fourier series that can adapt general coupling and boundary conditions is used to describe the displacement components of each spectral element. The generalized variation of the expansion coefficients yields the vibration equations of the built-up system. The convergence and accuracy of the method are validated through several numerical examples for various shell and plate combinations. The dynamic behaviors of the rotationally symmetric built-up structures are investigated by modal and forced vibration analysis. The method can predict the vibration responses of rotationally symmetric, built-up structures with low computational cost.

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Figures

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Fig. 1

Forces and moments at the junction of adjacent structures and operating principle of a three-dimensional elastic coupler

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Fig. 2

Multi-shell and plate-coupled structure and local coordinate systems for each substructure

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Fig. 3

Forces and moments at the ends of the substructures

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Fig. 4

Selected natural frequencies Ωmn and their corresponding mode shapes for the complete stiffened structure

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Fig. 5

Comparison of selected modal shapes Ωmn for the complete structure in three dimensions: (a) results of the developed method and (b) results from ansys

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Fig. 6

Nondimensional natural frequencies with increasing stiffness parameters

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Fig. 7

Natural frequencies of the complete structure with increasing numbers of ring stiffeners

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Fig. 8

Arrangement of Points O, A, B, C, D, and E and the driving force on the structure

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Fig. 9

Radial displacements at (a) point B and (b) point C due to the point force

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Fig. 10

Radial displacements of the structure at points A, B, D, and E

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