0
Research Papers

Analysis of Vibration of a Tank Caused by an Explosion

[+] Author and Article Information
M. Utsumi

Machine Element Department,
Technical Research Laboratory,
IHI Corporation,
1 Shinnakaharacho, Isogo ward,
Yokohama, Kanagawa 235-8501, Japan
e-mail: masahiko_utsumi@ihi.co.jp

H. Tazuke

Environment and Plants Operations,
IHI Corporation,
1-1, Toyosu 3-chome, Koto ward,
Tokyo 135-8710, Japan
e-mail: hideyuki_tazuke@ihi.co.jp

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received April 16, 2014; final manuscript received March 19, 2015; published online April 30, 2015. Assoc. Editor: Marco Amabili.

J. Vib. Acoust 137(5), 051006 (Oct 01, 2015) (16 pages) Paper No: VIB-14-1139; doi: 10.1115/1.4030186 History: Received April 16, 2014; Revised March 19, 2015; Online April 30, 2015

The vibration of a large tank caused by an explosion that occurs at a place apart from the tank is analyzed. Because the tank is double-walled and the liquid is contained in the inner shell, the vibration of the outer shell subjected to the explosion-induced pressure wave that travels outside the tank is analyzed without considering the liquid. A cylindrical tank with a spherical roof is considered as a realistic three-dimensional (3D) model, and a computationally efficient semi-analytical method that is applicable to the 3D geometry of the tank–fluid interface is investigated. First, cylindrical coordinates are introduced such that the longitudinal axis intersects the center of the tank base and is normal to the explosion source plane, thereby defining the inner and outer radii of the analysis domain of the fluid motion. Next, the solutions are expressed in terms of coordinate-dependent eigenvalues and a reduced order model is developed by applying the Galerkin method to the governing equations that take into account the compressibility and nonlinearity of the fluid motion. The method is verified by comparing with earlier results obtained by a numerical method. We also analyze the vibration of the tank shell by developing its finite element (FE) model and transforming the model into modal equations to develop a reduced order model for the fluid–tank system.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.

References

Ibrahim, R. A., Pilipchuk, V. N., and Ikeda, T., 2001, “Recent Advances in Liquid Sloshing Dynamics,” ASME Appl. Mech. Rev., 54(2), pp. 133–199. [CrossRef]
Hasheminejad, S. M., and Safari, N., 2005, “Acoustic Scattering From Viscoelastically Coated Spheres and Cylinders in Viscous Fluid,” J. Sound Vib., 280(1–2), pp. 101–125. [CrossRef]
Hasheminejad, S. M., and Kazemirad, S., 2008, “Dynamic Viscoelastic Effects on Sound Wave Scattering by an Eccentric Compound Circular Cylinder,” J. Sound Vib., 318(3), pp. 506–526. [CrossRef]
Doolittle, R. D., and Uberall, H., 1966, “Sound Scattering by Elastic Cylindrical Shell,” J. Acoust. Soc. Am., 39(2), pp. 272–275. [CrossRef]
Flax, L., and Neubauer, W. G., 1977, “Acoustic Reflection From Layered Elastic Absorptive Cylinders,” J. Acoust. Soc. Am., 61(2), pp. 307–312. [CrossRef]
Ferri, A. A., Ginsberg, J. H., and Roger, P. H., 1992, “Scattering of Plane Waves From Submerged Objects With Partially Coated Surfaces,” J. Acoust. Soc. Am., 92(3), pp. 1721–1728. [CrossRef]
Ginsberg, J. H., 2002, “On the Effect of Viscosity in Scattering From Partially Coated Infinite Cylinders,” J. Acoust. Soc. Am., 112(1), pp. 46–54. [CrossRef] [PubMed]
Cuschieri, J. M., 2006, “The Modeling of the Radiation and Response Green's Function of a Fluid-Loaded Cylindrical Shell With an External Compliant Layer,” J. Acoust. Soc. Am., 119(4), pp. 2150–2169. [CrossRef] [PubMed]
Mitri, F. G., 2006, “Acoustic Radiation Force Due to Incident Plane-Progressive Waves on Coated Cylindrical Shells Immersed in Ideal Compressible Fluids,” Wave Motion, 43(6), pp. 445–457. [CrossRef]
Denli, H., and Sun, J. Q., 2008, “Structural-Acoustic Optimization of Sandwich Cylindrical Shells for Minimum Interior Sound Transmission,” J. Sound Vib., 316(1–5), pp. 32–49. [CrossRef]
Johnson, W. M., and Cunefare, K. A., 2002, “Structural Acoustic Optimization of a Composite Cylindrical Shell Using FEM/BEM,” ASME J. Vib. Acoust., 124(3), pp. 410–413. [CrossRef]
Liu, C. H., and Chen, P. T., 2009, “Numerical Analysis of Immersed Finite Cylindrical Shells Using a Coupled BEM/FEM and Spatial Spectrum Approach,” Appl. Acoust., 70(2), pp. 256–266. [CrossRef]
Wu, C. J., 2002, “Double-Layer Structural-Acoustic Coupling for Cylindrical Shell by Using a Combination of WDA and BIE,” Appl. Acoust., 63(10), pp. 1143–1154. [CrossRef]
Renterghem, T. V., and Botteldooren, D., 2008, “Numerical Evaluation of Sound Propagating Over Green Roofs,” J. Sound Vib., 317(3–5), pp. 781–799. [CrossRef]
Liu, M., Liu, J., and Cheng, Y., 2014, “Free Vibration of a Fluid Loaded Ring-Stiffened Conical Shell With Variable Thickness,” ASME J. Vib. Acoust., 136(5), p. 051003. [CrossRef]
Shimamura, K., Toyoda, M., Takahashi, M., Yamaguchi, S., and Takuwa, D., 2005, “Example of Application of Numerical Simulation to the Blast Resistant Design of Cylindrical Tanks,” IHI Eng. Rev., 45(2), pp. 80–85.

Figures

Grahic Jump Location
Fig. 2

Tank shell element ij and its global displacement components (u¯,v¯,w¯) and local displacement components (u,v,w)

Grahic Jump Location
Fig. 3

Prescribed time variation in dynamic pressure at explosion source

Grahic Jump Location
Fig. 4

Distributions of dimensionless dynamic pressure p/pmax on tank–fluid interface. (a) Tank base z = 0 and (b) y = 0 along tank roof.

Grahic Jump Location
Fig. 5

Earlier results corresponding to Fig. 4

Grahic Jump Location
Fig. 6

Results corresponding to Fig. 5 for the case where ϕ and x derivatives of eigenvalues are not considered

Grahic Jump Location
Fig. 7

Results corresponding to Fig. 4(b) for smaller mode numbers: (a) the case where the mode number lmax in the x-direction is decreased from eight to six and (b) the case where the mode number kmax in the r-direction is decreased from five to three

Grahic Jump Location
Fig. 8

Results corresponding to Fig. 4(b) for the cases where the mode number nmax in the ϕ-direction is changed from two to one and 3: (a) nmax = 1 and (b) nmax = 3

Grahic Jump Location
Fig. 9

Results corresponding to Fig. 4(b) for the case where a polytropic ideal gas equation is used (γ = 1.25)

Grahic Jump Location
Fig. 10

Distributions along y = 0 on tank roof of: (a) normal displacement, (b) meridional membrane stress, and (c) circumferential membrane stress

Grahic Jump Location
Fig. 11

Results corresponding to Fig. 10(c) for the cases where the mode number mmax in the circumferential direction of the tank shell is changed from five to three and seven: (a) mmax = 3 and (b) mmax = 7

Grahic Jump Location
Fig. 12

Results corresponding to Fig. 10(c) for the case where the mode number qmax in the meridional direction of the tank shell is decreased from 20 to 14

Grahic Jump Location
Fig. 13

(a) Meridional and (b) circumferential bending stresses at y = 0 on tank roof for the cases where the mode number mmax in the circumferential direction is changed (qmax = 20)

Grahic Jump Location
Fig. 14

(a) Meridional and (b) circumferential bending stresses at y = 0 on tank roof for the case where the mode number qmax in the meridional direction is changed (mmax = 5)

Grahic Jump Location
Fig. 15

Distributions along y = 0 on tank roof of: (a) dimensionless dynamic pressure p/pmax and (b) circumferential membrane stress (case where tmax is decreased to 0.07925 s, i.e., 0.5 times the original value)

Grahic Jump Location
Fig. 16

Analogous effect of tmax on dimensionless dynamic pressure p/pmax. (a) tmax = 0.1585 s and (b) tmax = 0.07925 s.

Grahic Jump Location
Fig. 17

Distributions along y = 0 on tank roof of: (a) dimensionless dynamic pressure p/pmax, (b) normal displacement, and (c) circumferential membrane stress (case where explosion source approaches point source)

Grahic Jump Location
Fig. 18

Distributions along y = 0 on tank roof of: (a) normal displacement and (b) circumferential membrane stress (concrete tank, case where explosion source approaches point source)

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In