Numerical Determination of Minimum Mass Structures with Specified Natural Frequencies.

Abstract

The problem of the axial vibration of a cantilever beam is investigated both analytically and numerically. The mass distribution that minimizes the total mass for a given value of the frequency parameter beta is determined using both the sequential ordinary gradient-restoration algorithm (SOGRA) and the modified quasilinearization algorithm (MQA). Concerning the minimum value of the mass, SOGRA leads to a solution precise to at least 4 significant digits and MQA leads to a solution precise to at least 6 significant digits. Comparison of the optimal beam (a variable-section beam) with a reference beam (a constant-section beam) shows that the weight reduction depends strongly on the frequency parameter beta. This weight reduction is negligible for beta approaches 0, is 11.3% for beta = 1, is 55.3% for beta = 1.4, and approaches 100% for beta approaches pi/2. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1977
Accession Number
ADA053725

Entities

People

  • A. K. Wu
  • A. Mangiavacchi
  • Angelo Miele
  • B. P. Mohanty

Organizations

  • Rice University

Tags

Communities of Interest

  • Space

DTIC Thesaurus Topics

  • Air Force
  • Algorithms
  • Boundary Value Problems
  • Calculus Of Variations
  • Cantilever Beams
  • Computers
  • Differential Equations
  • Engineering
  • Equations
  • Frequency
  • Materials
  • Materials Science
  • Mechanical Engineering
  • Modulus Of Elasticity
  • Resonant Frequency
  • Vibration
  • Weight Reduction

Fields of Study

  • Physics

Readers

  • Analytical Mechanics
  • Operations Research
  • Structural Dynamics.