Free-Wave Propagation Relationships of Second-Order and Fourth-Order Periodic Systems

Abstract

This report develops an analytical expression for the determinant of two diagonally-indexed, full matrices when they are zero. These matrices originate from second- and fourth-order periodic system theory. The partial differential equations of these systems are solved using a series solution and are converted into closed-form analytical expressions The denominators of these expressions are zero when free-wave propagation is present, and these denominators are equated to the determinants of the system matrices derived from a second analytical method. This process develops a relationship between frequency and wavenumber that is explicit for free-wave propagation in these systems. Two examples are included to illustrate this new method.

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Document Details

Document Type
Technical Report
Publication Date
Apr 04, 2011
Accession Number
ADA542283

Entities

People

  • Andrew John Hull

Organizations

  • Naval Undersea Warfare Center

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Delta Functions
  • Department Of Defense
  • Differential Equations
  • Displacement
  • Equations
  • Frequency
  • Frequency Domain
  • Fungi
  • Information Operations
  • Mathematical Analysis
  • Modulus Of Elasticity
  • Partial Differential Equations
  • Real Variables
  • Rhode Island
  • Undersea Warfare
  • Wave Equations
  • Wave Propagation

Readers

  • Linear Algebra
  • Theoretical Analysis.
  • Wave Propagation and Nonlinear Chaotic Dynamics.