THE APPLICATION OF FOURIER ANALYSIS TO ONE DIMENSIONAL INITIAL VALUE PROBLEMS FOR VISCOELASTIC WAVE PROPAGATION.

Abstract

For one dimensional viscoelastic free vibration the necessary and sufficient condition that this problem is an eigenvalue problem requires that the wave number k squared be real and positive. This suggests Fourier representation for initial value problems with k as its integration variable. If the form e to the i(kx plus omega t) power is assumed as the elementary component of the solution, then, for each fixed k, the equation of motion reduces to a polynomial frequency equation for a discrete viscoelastic model. The roots omega(k)'s of the polynomial equation provide a complete set of elementary propagation components. It may happen that certain of the components do not possess the property of propagation but only of decay. It may also happen that in a certain range of k the component does not propagate, but for some other range of k it does. These properties give physical insight concerning the propagation and decay of the different components for an arbitrary viscoelastic disturbance. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1967
Accession Number
AD0820244

Entities

People

  • Shih-jung Chang

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Differential Equations
  • Doppler Effect
  • Eigenvalues
  • Equations
  • Fourier Analysis
  • Frequency
  • Frequency Shift
  • Mathematics
  • Polynomials
  • Vibration
  • 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)
  • Linear Algebra