A Closed Form Solution of a Longitudinal Beam With a Viscous Boundary Condition

Abstract

This paper develops a closed form solution of a longitudinal beam with a viscous boundary condition subjected to point loading. A new inner product is formulated that allows the time and space modes of the beam to decouple. This expansion yields explicit eigenvalues and eigenvectors. A frequency domain example is presented, and the results are compared with finite element solutions of the same problem. It is shown that the closed form solution is computationally more efficient than a finite element solution. Additionally, truncation error at lower frequencies is shown to be extremely small. The method is easily implemented and can provide time and frequency domain solutions to this class of problems.

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Document Details

Document Type
Technical Report
Publication Date
Apr 06, 1992
Accession Number
ADA248841

Entities

People

  • Andrew John Hull

Organizations

  • Naval Undersea Warfare Center

Tags

Communities of Interest

  • Air Platforms
  • Ground and Sea Platforms

DTIC Thesaurus Topics

  • Boundaries
  • Differential Equations
  • Dynamic Response
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Frequency
  • Frequency Domain
  • Frequency Response
  • Standards
  • Standing Waves
  • Truncation
  • Undersea Warfare
  • Wave Equations
  • Wave Power
  • Waves

Fields of Study

  • Engineering

Readers

  • Control Systems Engineering.
  • Linear Algebra
  • Structural Dynamics.

Technology Areas

  • Space