AXISYMMETRIC VIBRATIONS OF UNDERWATER SPHERICAL SHELLS

Free vibrations of spherical shells in water have been investigated. By applying Hamilton's principle, a pair of basic coupled equations of motion is derived based on the bending theory. For harmonic motions, these equations are combined into a single sixth-order nonhomogeneous differential equation of motion in normal displacement. For a shell vibrating in water, the displacement of the shell and the hydrodynamic pressure of the water field form an interaction problem which characterizes all vibration problems of underwater structures and is solved by introducing the velocity potential of the water field. At the interface of the shell and water, it is assumed that the normal velocity of the shell is equal to that of the water field. The frequency equations for axisymmetric free vibrations are derived and the mode shapes are obtained. In each case examples are given and the results are plotted.

• Supplemental Notes:
  • Sea Grant Technical Report #6
• Corporate Authors:

  University of Wisconsin, Madison

  Department of Engineering Mechanics
  Madison, WI  United States 
• Authors:
  • Chen, F C
  • Huang, T C
• Publication Date: 1971-6

Media Info

• Features: Figures; References;
• Pagination: 19 p.

Subject/Index Terms

• TRT Terms: Bending; Bending stress; Shells (Structural forms); Stresses; Vibration
• Old TRIS Terms: Elastic shells; Shell theory
• Subject Areas: Marine Transportation; Materials;

Filing Info

• Accession Number: 00019485
• Record Type: Publication
• Report/Paper Numbers: WIS-SG-71-206 Tech Rpt
• Files: TRIS
• Created Date: Nov 8 1972 12:00AM