Research Papers

A Domain Decomposition Method for Vibration Analysis of Conical Shells With Uniform and Stepped Thickness

[+] Author and Article Information
Yegao Qu

e-mail: quyegao@sjtu.edu.cn

Yong Chen

e-mail: chenyong@sjtu.edu.cn

Yifan Chen

e-mail: chenyifan0607@yahoo.com

Xinhua Long

e-mail: xhlong@sjtu.edu.cn

Hongxing Hua

e-mail: hhx@sjtu.edu.cn

Guang Meng

e-mail: gmeng@sjtu.edu.cn
State Key Laboratory of Mechanical
System and Vibration,
Shanghai Jiao Tong University,
Dongchuan Road No. 800, Shanghai 200240, PRC

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the Journal of Vibration and Acoustics. Manuscript received November 30, 2011; final manuscript received April 16, 2012; published online February 4, 2013. Assoc. Editor: Marco Amabili.

J. Vib. Acoust 135(1), 011014 (Feb 04, 2013) (13 pages) Paper No: VIB-11-1289; doi: 10.1115/1.4006753 History: Received November 30, 2011; Revised April 16, 2012

An efficient domain decomposition method is proposed to study the free and forced vibrations of stepped conical shells (SCSs) with arbitrary number of step variations. Conical shells with uniform thickness are treated as special cases of the SCSs. Multilevel partition hierarchy, viz., SCS, shell segment and shell domain, is adopted to accommodate the computing requirement of high-order vibration modes and responses. The interface continuity constraints on common boundaries and geometrical boundaries are incorporated into the system potential functional by means of a modified variational principle and least-squares weighted residual method. Double mixed series, i.e., the Fourier series and Chebyshev orthogonal polynomials, are adopted as admissible displacement functions for each shell domain. To test the convergence, efficiency and accuracy of the present method, free and forced vibrations of uniform thickness conical shells and SCSs are examined under various combinations of classical and nonclassical boundary conditions. The numerical results obtained from the proposed method show good agreement with previously published results and those from the finite element program ANSYS. The computational advantage of the approach can be exploited to gather useful and rapid information about the effects of geometry and boundary conditions on the vibrations of the uniform and stepped conical shells.

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Fig. 1

Domain decomposition model of a SCS with general boundary conditions

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Fig. 2

Frequency parameters Ωnm and mode shapes for the FS-EL SCS (values in parentheses are from ANSYS)

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Fig. 3

Frequency parameter variations versus circumferential wave number n for SCSs with different boundary conditions: (a) FS-FL; (b) FS-CL

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Fig. 4

A FS-CL SCS subjected to concentrated unit harmonic forces

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Fig. 5

Transfer receptances of point B for a FS-CL SCS: (a) s direction; (b) normal

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Fig. 6

Transfer receptances of point C for a FS-CL SCS: (a) s direction; (b) normal

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Fig. 7

Point receptances of point B for a FS-CL SCS: (a) s direction; (b) normal

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Fig. 8

Transfer receptances of point C for a FS-CL SCS: (a) s direction; (b) normal



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