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

Tags

DTIC Thesaurus Topics

  • Crystal Lattices
  • Crystal Structure
  • Crystals
  • Difference Equations
  • Equations
  • Frequency
  • Frequency Shift
  • Mathematical Analysis
  • Mathematics
  • Personality
  • Thickness
  • Vibration
  • Waves

Fields of Study

  • Physics

Readers

  • Quantum spin resonance or Electron Paramagnetic Resonance spectroscopy.
  • Structural Dynamics.