Simulation of a Moving Elastic Beam Using Hamilton's Weak Principle

Abstract

Hamilton's Law is derived in weak form for slender beams with closed cross sections. The result is discretized with mixed space-time finite elements to yield a system of nonlinear, algebraic equations. An algorithm is proposed for solving these equations using unconstrained optimization techniques, obtaining steady-state and time accurate solutions for problems of structural dynamics. This technique provides accurate solutions for nonlinear static and steady-state problems including the cantilevered elastica and flatwise rotation of beams. Modal analysis of beams and rods is investigated to accurately determine fundamental frequencies of vibration, and the simulation of simple maneuvers is demonstrated.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 2006
Accession Number
ADA449340

Entities

People

  • Elliott J. Leigh

Organizations

  • Air Force Institute of Technology

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Air Force
  • Constitutive Equations
  • Differential Equations
  • Equations
  • Finite Element Analysis
  • Frequency
  • Frequency Shift
  • Geometry
  • Mechanics
  • Modal Analysis
  • Modulus Of Elasticity
  • Nonlinear Algebraic Equations
  • Resonant Frequency
  • Simulations
  • Steady State
  • Three Dimensional
  • Two Dimensional

Fields of Study

  • Physics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Structural Dynamics.

Technology Areas

  • Space