On an Extension of the Galerkin Method to Nonconservative Stability Problems

Abstract

Based upon the concept of Galerkin's approximate method for solving eigenvalue problems, a new scheme of numerical treatment is proposed for a class of nonconservative (circulatory) elastic stability problems. This is accomplishe by considering, together with the original system, a second system which is obtained by introducing an adjoint to the circulatory force field. The resulting problem is shown to be self-adjoint, with eigenfunctions which possess the property of reducing the original problem to a simple integral equation. This integral equation may be solved by quadrature and an estimation of error is also possible. The proposed method is especially suitable for direct evaluation on a digital computer and does not involve tedious integrations of functions encountered in the commonly adopted application of the Galerkin method.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1972
Accession Number
AD0740565

Entities

People

  • George Herrmann
  • S. N. Prasad

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Air Force
  • Applied Mechanics
  • Boundary Value Problems
  • Classification
  • Differential Equations
  • Digital Computers
  • Eigenvalues
  • Equations
  • Galerkin Method
  • Integral Equations
  • Mechanics
  • Numerical Analysis
  • Real Variables
  • Scientific Research
  • Security
  • United States
  • Universities

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis