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Research Papers: Design and Analysis

Effects of Structural Perturbations on Strain Growth in Containment Vessels

[+] Author and Article Information
Q. Dong, B. Y. Hu

Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang 621900, P. R. China

Q. M. Li1

School of Mechanical, Aerospace and Civil Engineering, Pariser Building, The University of Manchester, P.O. Box 88, Manchester M60 1QD, UKqingming.li@manchester.ac.uk

J. Y. Zheng

Institute of Process Equipment, Zhejiang University, Hangzhou 310027, P. R. China

1

Corresponding author.

J. Pressure Vessel Technol 132(1), 011203 (Dec 23, 2009) (7 pages) doi:10.1115/1.4000372 History: Received June 02, 2009; Revised August 28, 2009; Published December 23, 2009; Online December 23, 2009

Strain growth is a phenomenon observed in the elastic response of containment vessels subjected to internal blast loading. The local dynamic response of a containment vessel may become larger in a later stage than its response in the initial breathing mode response stage. It has been reported in our previous study that bending modes may be excited after several cycles of breathing mode vibration, due to the dynamic instability in cylindrical and spherical shells without structural perturbations. The nonlinear modal coupling between the breathing mode and the excited bending mode is one of the causes for the strain growth observed in containment vessels. In this study, we demonstrate that, due to the existence of structural perturbations, various vibration modes may be excited in containment vessels in earlier response stage before the occurrence of nonlinear modal coupling. The linear superposition of the breathing mode and the vibration modes excited by structural perturbations may cause larger response than the pure breathing mode response, which is a different strain growth mechanism from the nonlinear modal coupling. In the later response stage when the nonlinear modal coupling happens, not only the breathing mode, but also the vibration modes excited by structural perturbations will interact nonlinearly with the bending modes excited by dynamic unstable vibration. Dynamic nonlinear finite element program, LS-DYNA , is employed to understand the effects of structural perturbations on strain growth in containment vessels subjected to internal blast loading.

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Figures

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Figure 1

The model of ring with structural perturbations

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Figure 2

Strain-time history for the response of Ring 1 subjected to impulsive loading (first peak strain is 0.006)

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Figure 3

Strain-time history for the response of Ring 2 subjected to impulsive loading (first peak strain is 0.006)

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Figure 4

(a) Strain-time history for the response of Ring 3 subjected to impulsive loading (first peak strain is 0.003). (b) The frequency spectrum of the strain-time history in Fig. 4.

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Figure 5

(a) Strain-time history for the response of the Ring 4 subjected to impulsive loading (first peak strain is 0.003). (b) The frequency spectrum of the strain-time history in Fig. 5.

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Figure 6

(a) Radial displacement-time history of the response of spherical Shell 1 subjected to impulsive loading (first peak strain is 0.005). (b) The frequency spectrum of the curve in Fig. 6.

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Figure 7

(a) Radial displacement-time history of the response at the pole of clamped hemispherical Shell 1 subjected to impulsive loading (first peak strain is 0.005). (b) The frequency spectrum of the curve in Fig. 7.

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Figure 8

A time-sequence snapshot of the deformed shapes of clamped hemispherical Shell 1 when first peak strain is 0.005 (the displacement has been amplified by a factor of 10): (a) 0 μs; (b) 10 μs; (c) 20 μs; (d) 30 μs; (e) 40 μs; (f) 50 μs; (g) 60 μs; (h) 70 μs; (i) 80 μs; (j) 90 μs; (k) 100 μs; (l) 110 μs

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Figure 9

The deformed shape of clamped hemispherical Shell 1 (the displacement has been amplified by a factor of 10)

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Figure 10

Radial displacement-time history at the pole of clamped hemispherical Shell 1 (first peak strain is 0.001) and one-fifth of radial displacement-time history at the pole of clamped hemispherical Shell 1 (first peak strain is 0.005)

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Figure 11

(a) Radial displacement-time history of the response of free-free cylindrical Shell A subjected to impulsive loading (first peak strain is 0.001). (b) The frequency spectrum of the curve in Fig. 1.

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