On the Analysis of Superharmonic Oscillations,

Abstract

This paper presents an analysis for the superharmonics of a forced nonlinear vibration problem involving small parameters, using a generalized harmonic balance method. A nonlinear ordinary differential equation with several nonlinear terms and a periodic forcing function is considered. For the case of superharmonic oscillations of order 2, the key equations for the obtaining the information on the superharmonics will be derived, including a new, nonlinear ordinary differential equation of a slow varying function compared with the original dependent variable. Using these equations, the steady state solution and its stability behavior can be calculated. Results for a special set of parameters are obtained, including a stable node for the steady state solution and the associated van del Pol plane.

Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1992
Accession Number
ADP006630

Entities

People

  • J. J. Wu

Organizations

  • Army Research Office

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Applied Mathematics
  • Differential Equations
  • Equations
  • Formulas (Mathematics)
  • Mathematics
  • Minnesota
  • Oscillation
  • Steady State
  • Vibration

Fields of Study

  • Mathematics

Readers

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