Nonlinear Periodic Waves in a Bounded Medium: A Regular Perturbation Approach.

Abstract

A regular perturbation scheme is given for calculating small amplitude nonlinear periodic waves in a medium of finite extent. The first term in the asymptotic expansion is an arbitrary linear standing wave. The signal carried by the waves is determined from the nonlinear terms in the governing equations by an application of the Fredholm alternative. This gives a systematic scheme for calculating the corrections to the basic flow. The first problem considered is the resonant forced motion of a polytropic gas contained in a tube with its end closed. The second problem concerns the free vibration of an anharmonic lattice, or a nonlinear dispersive string. (Author)

Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1970
Accession Number
AD0714997

Entities

People

  • Michael P. Mortell

Organizations

  • Lehigh University

Tags

DTIC Thesaurus Topics

  • Amplitude
  • Asymptotic Series
  • Equations
  • Mathematical Analysis
  • Mathematics
  • Perturbations
  • Standing Waves
  • Vibration
  • Waves

Fields of Study

  • Mathematics

Readers

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