## Vibration Characteristics of a Cylinder Partially Filled with Liquid with an Attached Elastic Drain Pipe, Volume 1490This report investigates liquid and ullage gas effects of a partially filled cylinder with attached elastic drain pipe. |

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### Contents

ANALYSIS OF THE CONTINUOUS SYSTEM | 7 |

COMPUTER PROGRAM | 16 |

Flexible Tank Bottom with Ullage Gas | 22 |

1 other sections not shown

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120 Liquid Height 25 Figure analysis APPENDIX asymmetric breathing axisymmetric Bottom with Ullage bulk modulus computer program computer run COORDS Cylindrical data points displacement coordinate displacements selected drain pipe EIGENVALUES EIGENVECTORS equation 11 equation ref Figure 17 Figure 18 Flexible Bottom Flexible Tank Bottom free surface frequencies and mode frequencies versus liquid frequency curves fundamental frequency input Integration parameter kinetic energy Lagrange's equation Langley Research Center length or pipe liquid fueled launch Liquid Height inches longitudinal vibrations lowest frequencies versus MATRIX T(I,J mode shapes NASA parameter in equation parametric studies pipe radius pipe wall thickness placements potential energy pressure radial coordinate Rayleigh-Lagrange Rigid Bottom Rigid Tank Bottom shown in Figure standard configuration stiffness strain energy structural frequencies structural motion t)sin(A tank and pipe tank radius tank wall thickness ullage gas effects uncoupled frequency University of Cincinnati Variable Pipe Lengths Variable Tank Radii velocity potential function versus liquid height