Dynamics of Elastic Foundations and Constrained Bars

Abstract

A variational principle is used to derive the equations of motion of a slender bar that has one lateral face clamped (or welded) onto a rigid surface. Correction factors for the transverse shear and normal strains are incorporated into the expression for the strain energy of the system. These factors are evaluated by requiring the lowest depth-shear and depth-stretch frequencies, as derived from the new approximate theory, to agree with the corresponding frequencies obtained from the full theory of generalized plane stress. The frequency equation for a simple supported constrained bar is derived, and plots of the variations of the natural frequencies of the transverse and longitudinal modes versus the length to depth ratio of the bar are presented.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1976
Accession Number
ADA026404

Entities

People

  • G. L. Anderson

Tags

Communities of Interest

  • Air Platforms
  • C4I
  • Weapons Technologies

DTIC Thesaurus Topics

  • Boundary Value Problems
  • Classification
  • Differential Equations
  • Dynamic Response
  • Dynamics
  • Equations
  • Equations Of Motion
  • Frequency
  • Lagrangian Functions
  • Modulus Of Elasticity
  • Partial Differential Equations
  • Resonant Frequency
  • Security
  • Stress Strain Relations
  • Transient Response Analysis
  • Transverse
  • Vibration

Readers

  • Electrical Engineering
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Materials Science and Engineering.