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An analytic model for the water blast response of one-dimensional marine structure coated with elastic foam

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Abstract

The water blast response of one-dimensional marine structures coated with elastic foam is theoretically investigated. The foam coating is modeled by a group of concentrated masses separated by parallel massless nonlinear spring and damper, simulating the micro inertia, stiffness, and rate-dependent effects exhibited by common cellular materials. An analytic model for the wet face response, inclusive of fluid-structure interaction, is developed. The model addresses cavitation and takes into account the momentum of reconstituted water attached to the wet face. The first-order double asymptotic approximation method is used to compute the pressure during the spring-back and succeeding phase. The fidelity of the analytic model has been assessed by the finite element analysis.

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Abbreviations

L :

the thickness of the foam core

h b :

the thickness of steel plate

h f :

the thickness of the front plate

A :

the cross-section area of the foam core

ΔL :

the thickness of a single piece of foam core

N :

the number of pieces divided of the foam core

ρ * :

the density of foam

ρ s :

the density of solid cell wall material

m i :

the mass of a single piece of foam

m b :

the mass of back panel

m f :

the mass of front plate

k i :

the stiffness of a single piece of foam

K s :

the stiffness of the supporting structure

σ ( ):

nonlinear strain–stress relation of foam

C1, D, p:

material constants

\({\sigma_{el}^\ast}\) :

the elastic buckling stress of foam

E * :

the linear elastic modulus of foam

E s :

the elastic modulus of solid cell wall material

ε b :

the critical strain at which buckling begins

ε D :

the densification strain of foam

p(t):

the total pressure acted on the front panel

P i (t):

the incident pressure produced by underwater explosion

P 0 :

the pressure peak of the incident pressure

θ :

the decaying constant of the incident pressure

β :

the fluid/structure interaction parameter

M f , A f :

the fluid mass matrix and area matrix of the boundary elements

ρ w , c w :

the density and sound speed of water

c :

the proportional damping factor

t c , t r :

some dividing moments defined for convenience

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Authors and Affiliations

  1. Institute of Vibration, Shock and Noise, Shanghai Jiao Tong University, 800 Dong Chuan Road, 200240, Shanghai, People’s Republic of China

    Yong Chen & Hong Xing Hua

  2. Naval Academy of Armament, 100073, Beijing, People’s Republic of China

    Yu Wang

Authors
  1. Yong Chen
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  2. Yu Wang
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  3. Hong Xing Hua
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Correspondence to Yong Chen.

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Chen, Y., Wang, Y. & Hua, H.X. An analytic model for the water blast response of one-dimensional marine structure coated with elastic foam. Arch Appl Mech 80, 1243–1253 (2010). https://doi.org/10.1007/s00419-009-0367-1

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  • DOI: https://doi.org/10.1007/s00419-009-0367-1

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