Acceleration Wave Propagation in Hyperelastic Rods of Variable Cross-Section.

Abstract

It is shown that when an acceleration wave propagates in a hyperelastic rod with slowly varying cross-section, the transport equation for the wave intensity is a generalized Riccati equation. The three coefficients in the equation all depend on the material properties, but only the coefficient of the quadratic term is independent of the effect of area change. Three theorems are proved, based on the use of comparison equations, which establish that in general the acceleration wave intensity will become infinite (escape) after the wave has propagated only a finite distance along the rod. The existence of thresholds for the initial intensity are also established in certain cases, with their most notable property being that as the initial intensity decreases towards the threshold, so the distance the wave propagates to escape increases without bound. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1981
Accession Number
ADA103878

Entities

People

  • A. Jeffrey

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Boltzmann Equation
  • Coefficients
  • Differential Equations
  • Displacement
  • Elastic Materials
  • Electrical Solitons
  • Equations
  • Intensity
  • Materials
  • Mathematics
  • Riccati Equation
  • Shock
  • Shock Waves
  • Transport Ships
  • United States
  • Universities
  • Wave Propagation

Fields of Study

  • Mathematics

Readers

  • Control Systems Engineering.
  • Mechanical Engineering/Mechanics of Materials.
  • Wave Propagation and Nonlinear Chaotic Dynamics.