Analytical Solutions for Open Nonshallow Spherical Shell Vibrations
Abstract
This report is concerned with axisymmetric as well as nonsymmetric vibrations of open nonshallow thin elastic spherical shells. Without employing the usual auxiliary variables for reduction of shell motion equations introduced by Van der Neut and Berry, independent analytical solutions for middle-surface displacements are obtained and explicitly expressed in terms of associated Legendre functions. In order to gain physical insights into the free-vibration characteristics of an open nonshallow shell, theoretical calculations together with asymptotic descriptions are made of natural frequencies and mode shapes of a hemispherical shell with a free edge. Five families of natural frequencies, i. e., low Rayleigh bending, mixed bending-membrane, torsional, bending and membrane frequencies, are found. The corresponding mode shapes exhibit distinctive displacement patterns.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1979
- Accession Number
- ADA074269
Entities
People
- Gau-feng Lin