Equations of Motion for Nonaxisymmetric Vibrations of Prolate Spheroidal Shells

Abstract

This report documents the derivation of the equations for nonaxisymmetric motion of prolate spheroidal shells of constant thickness. The equations include the effect of distributed mechanical surface forces and moments. These equations were derived from the Lagrangian of the system. The thin shell theory used in this derivation includes three displacements and two changes of curvature. Thus, the effects of membrane, bending, shear deformations, and rotatory inertias are included in this theory. The resulting five coupled partial differential equations are self-adjoint and positive definite, ensuring real and positive eigenvalues and real eigenfunctions. The frequency-wavenumber spectrum has five branches (three acoustic and two optical) representing flexural, longitudinal, torsional, and thickness-shear modes. The acoustic branches have the correct group and phase velocities, especially in the high wavenumber, short wavelength limits.

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Document Details

Document Type
Technical Report
Publication Date
Feb 18, 2000
Accession Number
ADA377034

Entities

People

  • Jeffrey E. Boisvert
  • Sabih I. Hayek

Organizations

  • Naval Undersea Warfare Center

Tags

Communities of Interest

  • Energy and Power Technologies
  • Ground and Sea Platforms

DTIC Thesaurus Topics

  • Computational Science
  • Coordinate Systems
  • Curvature
  • Differential Equations
  • Eigenvalues
  • Equations Of Motion
  • Frequency
  • Geometric Forms
  • Geometry
  • Mechanics
  • Partial Differential Equations
  • Phase Velocity
  • Stress Strain Relations
  • Two Dimensional
  • Vibration
  • Wave Functions
  • Waves

Readers

  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Calculus or Mathematical Analysis
  • Structural Dynamics.