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Research Papers

The Response of Rigid Plates to Deep Water Blast: Analytical Models and Finite Element Predictions

[+] Author and Article Information
A. Schiffer, N. Petrinic, A. C. F. Cocks

 Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK

V. L. Tagarielli

 Department of Aeronautics, Imperial College London, South Kensington Campus,London SW5 2AZ, UKv.tagarielli@imperial.ac.uk

J. Appl. Mech 79(6), 061014 (Sep 21, 2012) (14 pages) doi:10.1115/1.4006458 History: Received April 14, 2011; Revised December 07, 2011; Posted March 29, 2012; Published September 21, 2012; Online September 21, 2012

One-dimensional analytical models and finite element calculations are employed to predict the response of a rigid plate, supported by a linear spring, to loading by a planar pressure shock wave traveling in water or in a similar inviscid liquid. Two problems are considered: (i) a spring-supported rigid plate in contact with fluid on one side and (ii) a spring-supported rigid plate in contact with fluid on both sides; for both problems, plates are loaded by an exponentially decaying shock wave from one side. Cavitation phenomena in the liquid, as well as the effect of the initial static fluid pressure, are explicitly included in the analytical models and their predictions are found to be in excellent agreement with those from FE calculations. The validated analytical models are used to determine the sensitivity of the plate’s response to mass, spring stiffness and initial static pressure.

Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Sketches of problem geometry, reference system, boundary conditions and loading case for Problems 1 (a) and 2 (b)

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Figure 2

(a) Schematic illustration of the phenomena of initial cavitation, emergence, and propagation of breaking fronts, development of a closing front. (b) Detail of the fluid conditions at a propagating closing front.

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Figure 3

Nondimensional regime charts for Problem 1. The curves show the transitions between different regimes for two different values of nondimensional static pressure, p¯st=0 (a) and p¯st=0.6 (b).

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Figure 4

Nondimensional regime charts for Problem 2. The curves show the transitions between different regimes for two different values of nondimensional static pressure, p¯st=0 (a) and p¯st=0.07 (b).

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Figure 5

Schematic of the one-dimensional abaqus explicit FE simulations conducted in this study to investigate water-backed plate response (Problem 2). FE simulations for Problem 1 follow a similar scheme with the fluid column attached to the plate’s back face absent.

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Figure 6

Nondimensional time versus position charts illustrating, for Problem 1, emergence of cavitation in the fluid attached to the plate’s front face and subsequent propagation of breaking fronts and closing fronts: (a) effect of nondimensional stiffness and (b) effect of the initially applied pressure

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Figure 7

Analytical and FE predictions of the nondimensional front face pressure and plate velocity time histories for Problem 1, regime 1, corresponding to ψ=2.5, κ=0.004, p¯st=0.6

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Figure 8

Analytical and FE predictions of the nondimensional front face pressure and plate velocity time histories for Problem 1, regime 2, corresponding to ψ=2.5, κ=0.2, p¯st=0

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Figure 9

Analytical and FE predictions of the nondimensional front face pressure and plate velocity time histories for Problem 1, regime 3, corresponding to ψ=2.5, κ=0.004, p¯st=0

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Figure 10

Nondimensional time versus position charts illustrating, for Problem 2, emergence of cavitation in the fluid attached to the plate’s front face and subsequent propagation of breaking fronts and closing fronts: (a) effect of nondimensional stiffness and (b) effect of the initially applied pressure

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Figure 11

Analytical and FE predictions of the nondimensional front face pressure, back face pressure, and plate velocity time histories for Problem 2, regime 1, corresponding to ψ=2.8, κ=0.03, p¯st=0.07. The fluid does not cavitate.

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Figure 12

Analytical and FE predictions of the nondimensional front face pressure, back face pressure, and plate velocity time histories for Problem 2, regime 2, corresponding to ψ=2.8, κ=0.17, p¯st=0. The fluid initially cavitates at the back face.

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Figure 13

Analytical and FE predictions of the nondimensional front face pressure, back face pressure, and plate velocity time histories for Problem 2, regime 3, corresponding to ψ=2.8, κ=0.11, p¯st=0. The fluid initially cavitates in the front region and subsequently at the back face.

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Figure 14

Analytical and FE predictions of the nondimensional front face pressure, back face pressure, and plate velocity time histories for Problem 2, regime 4, corresponding to ψ=2.8, κ=0.03, p¯st=0. The fluid initially cavitates in the front region and subsequently at the back face.

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Figure 15

(a) Problem 1: partial and total nondimensional impulse imparted to the front face as a function of nondimensional stiffness κ, for selected values of p¯st. (b) Problem 1: partial and total nondimensional impulse imparted to the front face as a function of the nondimensional parameter ψ, for selected values of p¯st.

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Figure 16

(a) Problem 2: partial and total nondimensional impulse imparted to the front face as a function of nondimensional stiffness κ, for selected values of p¯st. (b) Problem 2: total nondimensional impulse applied to the front face as a function of the nondimensional parameter ψ, for selected values of p¯st. It=Ip in this case.

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