LATTICE AND CONTINUUM THEORIES OF SIMPLE MODES OF VIBRATION IN CUBIC CRYSTAL PLATES AND BARS.
Abstract
With a view toward helping to bridge the gap, from the discrete side, between discrete and continuum models of crystalline, elastic solids, analytic solutions, in closed form, are obtained of the Gazis-Herman-Wallis finite difference equations of a simple cubic, crystal lattice for the cases of thickness-shear vibrations of a plate, face-shear and thickness-twist waves in a plate and axial shear vibrations of a rectangular bar. The simple character of the solutions facilitates detailed studies of frequencies and mode-shapes as the dimensions of the bodies and wave lengths increase from atomic to the macroscopic sizes at which the classical continuum theory may be used. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1968
- Accession Number
- AD0677041
Entities
People
- Raymond D. Mindlin
Organizations
- Columbia University