ON LONGITUDINAL AND TRANSVERSE WAVES IN ELASTIC RODS,

Abstract

The approximate equations governing the longitudinal and transverse motions of elastic rods are derived from the exact equations of motion of an elastic solid by making certain assumptions about the deformations in the rod. Both the slab (two-dimensional plane strain problem) and the circular cylindrical rod are considered. It is found that the equations for longitudinal waves agree with those obtained by Mindlin and Herrman, and by Volterra. In the case of transverse waves, it is found that there is a fundamental difference between the equations derived in this report and those of Timoshenko and Flugge. The present theory predicts that discontinuities in moment are propagated at the dilatational velocity, and that discontinuities in shear force are propagated at the shear velocity. The corresponding velocities in the Timoshenko-Flugge theory are both smaller. (Author)

Document Details

Document Type
Technical Report
Publication Date
Nov 10, 1954
Accession Number
AD0631816

Entities

People

  • H. J. Plass Jr.

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Discontinuities
  • Equations
  • Equations Of Motion
  • Mathematics
  • Transverse
  • Transverse Waves
  • Two Dimensional
  • Waves

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Structural Dynamics.