Stability of a System of Three Degrees of Freedom Subjected to a Circulatory Force,

Abstract

The free vibrations of a uniformly accelerating linear elastic, nondissipative system of three degrees of freedom, carrying a tip mass and subjected to a constant circulatory thrust applied at a free end, are investigated for the purpose of determining the influence of the orientation of the thrust on the system's state of stability. A thrust orientation parameter alpha is introduced to reflect the conservative and nonconservative components of the applied thrust. A dimensionless bi-cubic frequency equation whose coefficients depend upon the tip mass, and thrust orientation parameters is solved and eigen-curves are plotted for several values of alpha. These eigencurves reveal that the system becomes unstable by divergence for any positive thrust, no matter how small, whenever the value of alpha is such that the system can be classified as pseudo-conservative. There also exists a range of alpha for which the system is first unstable by divergence, secondly stable, and finally unstable by flutter as the magnitude of the thrust is increased. For alpha sufficiently large, the system is stable for a certain range of values of the thrust, but eventually it becomes unstable by flutter as the thrust is increased beyond its critical value.

Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1975
Accession Number
ADA020809

Entities

People

  • G. L. Anderson

Tags

DTIC Thesaurus Topics

  • Coefficients
  • Doppler Effect
  • Equations
  • Frequency
  • Frequency Shift
  • Motion
  • Orientation (Direction)
  • Vibration

Fields of Study

  • Physics

Readers

  • Control Systems Engineering.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)