Generalized-alpha Time Integration Solutions for Hanging Chain Dynamics

Abstract

In this paper, we study numerically the two and three-dimensional nonlinear dynamic response of a chain hanging under its own weight. Previous authors have employed the box method, a finite-difference scheme popular in cable dynamics problem, for this purpose. The box method has significant stability problems, however, and thus is not well suited to that highly nonlinear problem. We illustrate these stability problems and propose a new time integration procedure based on the generalized-alpha method. The new method exhibits superior stability properties compared to the box method and other algorithms such as backward differences and trapezoidal rule. Of four time integration methods tested, the generalized-alpha algorithm was the only method that produced a stable solution for the three-dimensional whirling motions of a hanging chain driven by harmonic linear horizontal motion at the top.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 2002
Accession Number
ADA408357

Entities

People

  • Jason I. Gobat
  • Mark A. Grosenbaugh
  • Michael S. Triantofyllou

Organizations

  • Woods Hole Oceanographic Institution

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Algorithms
  • Coefficients
  • Computer Programs
  • Difference Equations
  • Differential Equations
  • Dynamic Response
  • Dynamics
  • Eigenvalues
  • Engineering
  • Equations
  • Finite Element Analysis
  • Frequency
  • Geometry
  • Mechanics
  • Power Spectra
  • Three Dimensional
  • Two Dimensional

Readers

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