Analysis of the Non-Planar Response of a Cantilever, with the Aid of Computerized Symbolic Manipulation

Abstract

The nonlinear differential equations governing the static deformations of a cantilever with a tip mass are formulated and analyzed with the aid of computerized symbolic manipulation. The nonlinearities in the equations are geometric and include terms such as nonlinear contributions to the curvature expression. All the algebra in this work is relegated to the computer. Most of the work presented in the literature dealing with the response of structural elements such as beams is restricted to planar response. In addition, much of the work is also restricted to the cases where the deformations are very small and are analyzed by linear theory. In general, a structure can undergo flexure in any direction in space, and torsion. For infinitesimally small deformations, flexural and torsional motions are uncoupled. In this paper the flexural-flexural-torsional deformations on a cantilever with a tip mass are determined. Reprints.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1988
Accession Number
ADA212421

Entities

People

  • James K. Nelson Jr.
  • M. R. Crespo Da Silva

Organizations

  • Rensselaer Polytechnic Institute

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Aeronautical Engineering
  • Computers
  • Curvature
  • Differential Equations
  • Engineering
  • Equations
  • Geometric Forms
  • Geometry
  • Lines (Geometry)
  • Mechanical Engineering
  • Military Research
  • Nonlinear Differential Equations
  • Plastic Explosives

Readers

  • Calculus or Mathematical Analysis
  • Structural Dynamics.

Technology Areas

  • Space