THE PROPAGATION OF SHOCK WAVES IN SEMILINEAR VISCOELASTIC MATERIALS.

Abstract

A nonlinear viscoelastic material whose constitutive functional is represented by a multiple integral expansion, with the characteristic property that the instantaneous response is linear, is called semilinear. It is shown that, in a longitudinal impact on the end of a long bar of such a material, the velocity (or stress) is governed by a nonlinear integro-differential equation. If the velocity (or stress) is prescribed at the end of the bar, then the solution may be obtained in the form of a traveling wave, with the state variables behind the wave front expressed in the form of power series whose coefficients are obtainable by quadratures. A sample calculation exhibits the quantitative effects of nonlinear memory on wave propagation. The method used in the paper is also shown to be extendable to certain problems of three dimensional wave propagation. (Author)

Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1966
Accession Number
AD0489745

Entities

People

  • G. A. Secor
  • J. Lubliner

Organizations

  • University of California, Berkeley

Tags

DTIC Thesaurus Topics

  • Coefficients
  • Differential Equations
  • Equations
  • Integrals
  • Materials
  • Mathematics
  • Power Series
  • Shock
  • Shock Waves
  • Three Dimensional
  • Traveling Waves
  • Wave Propagation
  • Waves

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Combustion Dynamics and Shock Wave Physics.
  • Structural Dynamics.