The Use of Eigen-Derivatives to Predict the Effect of Design Changes Upon the Dynamic Characteristics of Structural Elements.

Abstract

Equations relating the changes in the eigenvalues and eigenfunctions of a freely vibrating system due to changes in that system's physical configuration are derived from the integral formulation of the eigenvalue problem. These expressions are used to determine the natural frequencies and mode shapes of several non-uniform structural elements. The problems investigated include longitudinal motion of a stepped and linearly tapered bar, and the transverse motion of simply supported tapered and symmetrically shaped beams. The equations are used in conjuction with a first order Taylor series marching process to determine the change in system characteristics as the system's physical parameters change. For the systems investigated, this eigenderivative method produced good frequency and mode shape predictions for both the fundamental mode and the higher modes.

Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1974
Accession Number
ADA005281

Entities

People

  • James L. Vick

Organizations

  • Air Force Institute of Technology

Tags

DTIC Thesaurus Topics

  • Differential Equations
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Frequency
  • Integrals
  • Mathematics
  • Resonant Frequency
  • Transverse

Fields of Study

  • Physics

Readers

  • Fluid Dynamics.
  • Ocean-Atmosphere Mesoscale Modeling, Data Assimilation, and Flux Boundary Layers
  • Structural Dynamics.