An Averaging Technique for the Analysis of Oscillations in Abruptly Nonlinear Systems,

Abstract

An approximate technique, based on a new generalization of the method of equivalent linearization, is presented for analysis of oscillations in such abruptly nonlinear system as those involving vibroimpact between adjacent structures. The new method introduces a weighting function into the averaging integrals used in the familiar method of equivalent linearization. The weighting is chosen such that the free vibration backbone curve of the approximate solution matches that of the exact solution at an arbitrary number of preselected amplitudes. Both one- and two-degree-of-freedom (DOF) examples involving periodic motion of colliding oscillators are presented to illustrate the nature of the results. Contact forces are modeled both by a unilateral linear spring and dashpot and by impulse/momentum and coefficient of restitution approaches. It is shown that an approximate amplitude-frequency response curve of adequate accuracy can be obtained with a computational effort several orders of magnitude less than that required by direct numerical simulation. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1984
Accession Number
ADP003665

Entities

People

  • M. A. Heidari
  • R. K. Miller

Organizations

  • University of Southern California

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Amplitude
  • Coefficients
  • Dynamics
  • Frequency
  • Frequency Response
  • Frequency Shift
  • Integrals
  • Momentum
  • Nonlinear Systems
  • Oscillation
  • Oscillators
  • Simulations
  • Spine
  • Universities
  • Weighting Functions

Readers

  • Calculus or Mathematical Analysis
  • Control Systems Engineering.
  • Structural Dynamics.