Stresses in a Cylinder Subjected to an Internal Shock

[+] Author and Article Information
Robert A. Leishear

 Washington Savannah River Company, Aiken, SC 29808robert.leishear@SRS.gov

J. Pressure Vessel Technol 129(3), 372-382 (Jan 21, 2007) (11 pages) doi:10.1115/1.2748820 History: Received January 24, 2006; Revised January 21, 2007

Hoop stresses due to a moving shock front in either a gas or liquid filled cylinder can be approximated using vibration theory. The equation of motion can be combined with hoop stress equations to describe the dynamic changes in hoop stress to provide insight into the phenomenon of flexural resonance, which creates pipe stresses significantly in excess of the stresses expected from a slowly applied, or static, pressure loading. To investigate flexural resonance, vibration equations were successfully compared to available experimental results. At shock velocities, the maximum hoop stress is related to a vibration equation for a suddenly applied load. Consideration of structural and fluid damping, as well as pipe constraints at the end of the pipe, were considered in the derivation of the vibration equations. In short, vibration equations are presented in this paper and are compared to available experimental work. The equations describe hoop stresses in a pipe when a step increase in pressure travels the bore of a pipe at sonic or supersonic velocities.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

Model for pipe wall vibration

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Figure 2

Pressure behind the shock wave in the tube (2)

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Figure 3

Strains at a point on the outer pipe wall (shock velocity=3278ft∕s) (2)

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Figure 4

Strains at a point on the outer pipe wall (shock velocity=3175ft∕s) (2)

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Figure 5

Example of dynamic amplification data (14)

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Figure 6

Relationship between dynamic amplification factor and thermodynamic states for a step response

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Figure 7

Step response of the hoop strain to a suddenly applied pressure

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Figure 8

Hoop strain due to through wall compression

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Figure 9

Step pressure which creates the precursor vibration

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Figure 10

Maximum precursor strain due to vibration

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Figure 11

Relationship between free vibrations before and after the shock

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Figure 12

Maximum free vibration after the shock

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Figure 13

Maximum hoop strain due to a shock wave traveling above the critical velocity (3278ft∕s) at the pipe O.D., M=2.908

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Figure 14

Maximum hoop stress at the pipe O.D.

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Figure 15

Maximum hoop stress at the pipe I.D.

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Figure 16

Calculated aftershock strains at a point on the pipe where the strains of Figs.  34 were measured

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Figure 17

Calculated aftershock strains at a different point on the pipe wall

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Figure 18

Maximum strain at M=1.1

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Figure 19

Maximum strain at M=1.44

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Figure 20

Maximum strain at M=5



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