LONGITUDINAL WAVE PROPAGATION ON A TRAVELING THREADLINE I,

Abstract

The nonlinear equations of motion governing the longitudinal wave propagation on a moving elastic string are presented. These are analyzed using three mathematical techniques. The first employs a von Mises type of transformation from the physical to the particle function - time plane. The resulting equations are shown to be equivalent to the linear wave equation thus permitting construction of the general solution. Secondly, auxiliary functions are employed but the resulting Monge-Ampere equation is more difficult to solve than the original quasilinear equation. Lastly the quasilinear theory provides a vehicle for transforming the problem into a linear problem for time and space in the Riemann invariants plane. An example pure initial value problem, solved exactly, displays the effect of a critical velocity on the system. (Author)

Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1968
Accession Number
AD0697736

Entities

People

  • A. A. Vicario Jr
  • W. F. Ames

Organizations

  • University of Iowa

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Construction
  • Differential Equations
  • Equations
  • Equations Of Motion
  • Mathematics
  • Military Vehicles
  • Partial Differential Equations
  • Particles
  • Vehicles
  • Vibration
  • Wave Equations
  • Wave Propagation
  • Waves

Fields of Study

  • Mathematics

Readers

  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)

Technology Areas

  • Space