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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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References

Irie, T., Yamada, G., and Kaneko, Y., 1982, “Free Vibration of a Conical Shell With Variable Thickness,” J. Sound Vib., 82(1), pp.83–94. [CrossRef]
Grigorenko, A. Ya., and Mal'tsev, S. A., 2009, “Natural Vibrations of Thin Conical Panels of Variable Thickness,” Int. Appl. Mech., 45(11), pp.1221–1231. [CrossRef]
Liew, K. M., Lim, M. K., Lim, C. W., Li, D. B., and Zhang, Y. R., 1995, “Effects of Initial Twist and Thickness Variation on the Vibration Behaviour of Shallow Conical Shells,” J. Sound Vib., 180(2), pp.271–296. [CrossRef]
Harintho, H., and Logan, D. L., 1988, “Conical Shells With Discontinuities in Geometry,” J. Struct. Eng., 114(1), pp.231–240. [CrossRef]
Wan, F. Y. M., 1970, “On the Equations of the Linear Theory of Elastic Conical Shells,” Stud. Appl. Math., XLIX(1), pp.69–83.
Tong, L. Y., 1993, “Free Vibration of Composite Laminated Conical Shells,” Int. J. Mech. Sci., 35(1), pp.47–61. [CrossRef]
Shu, C., 1996, “An Efficient Approach for Free Vibration Analysis of Conical Shells,” Int. J. Mech. Sci., 38(8–9), pp.935–949. [CrossRef]
Liew, K. M., Ng, T. Y., and Zhao, X., 2005, “Free Vibration Analysis of Conical Shells via the Element-Free kp-Ritz Method,” J. Sound Vib., 281(3–5), pp.627–645. [CrossRef]
Lim, C. W., and Liew, K. M., 1995, “Vibratory Behaviour of Shallow Conical Shells by a Global Ritz Formulation,” Eng. Struct., 17(1), pp.63–70. [CrossRef]
Lim, C. W., and Liew, K. M., 1996, “Vibration of Shallow Conical Shells With Shear Flexibility: A First-Order Theory,” Int. J. Solids Struct., 33(4), pp.451–468. [CrossRef]
Petyt, M., and Gélat, P. N., 1998, “Vibration of Loudspeaker Cones Using the Dynamic Stiffness Method,” Appl. Acoust., 53(4), pp.313–332. [CrossRef]
Chung, H., 1981, “Free Vibration Analysis of Circular Cylindrical Shells,” J. Sound Vib., 74(3), pp.331–350. [CrossRef]
Chang, S. D., and Greif, R., 1979, “Vibrations of Segmented Cylindrical Shells by a Fourier Series Component Mode Method,” J. Sound Vib., 67(3), pp.315–328. [CrossRef]
Monterrubio, L. E., 2009, “Free Vibration of Shallow Shells Using the Rayleigh–Ritz Method and Penalty Parameters,” Proc. IMechE. Part C: J. Mech. Eng. Sci., 223(10), pp.2263–2272. [CrossRef]
Amabili, M., 1997, “Shell-Plate Interaction in the Free Vibrations of Circular Cylindrical Tanks Partially Filled With a Liquid: the Artificial Spring Method,” J. Sound Vib., 199(3), pp.431–452. [CrossRef]
Amabili, M., 1998, “Rayleigh Quotient, Ritz Method and Substructuring to Study Vibrations of Structures Coupled to Heavy Fluids: Potential of the Artificial Spring Method,” Flow. Turbul. Combust., 61(1–4), pp.21–30. [CrossRef]
Missaoui, J., and Cheng, L., 1999, “Vibroacoustic Analysis of a Finite Cylindrical Shell With Internal Floor Partition,” J. Sound Vib., 226(1), pp.101–123. [CrossRef]
Chien, W. Z., 1983, “Method of High-Order Lagrange Multiplier and Generalized Variational Principles of Elasticity With More General Forms of Functionals,” Appl. Math. Mech., 4(2), pp.143–157. [CrossRef]
Washizu, K., 1982, Variational Methods in Elasticity and Plasticity, 3rd ed., Pergamon, New York, Chap. 2.
Leissa, A. W., 1973, Vibration of Shells (NASA SP-288), Government Printing Office, Washington, DC, Chap. 1.
Dupire, G., Boufflet, J. P., Dambrine, M., and Villon, P., 2010, “On the Necessity of Nitsche Term,” Appl. Numer. Math., 60(9), pp.888–902. [CrossRef]
Pellicano, F., 2007, “Vibrations of Circular Cylindrical Shells: Theory and Experiments,” J. Sound Vib., 303(1–2), pp.154–170. [CrossRef]
Zhou, D., Cheung, Y. K., Lo, S. H., and Au, F. T. K., 2003, “3D Vibration Analysis of Solid and Hollow Circular Cylinders via Chebyshev–Ritz Method,” Comput. Methods Appl. Mech. Eng., 192(13–14), pp.1575–1589. [CrossRef]
Petyt, M., 1990, Introduction to Finite Element Vibration Analysis, Cambridge University, Cambridge, England, Chap. 9.

Figures

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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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