Ideal Solution of an Inverse Normal Mode Problem with Finite Spectral Data.

Abstract

The problem of reconstructing the density of a vibrating string given the first N eigenfrequencies for two vibrating configurations admits an infinite number of solutions. Among all such strings compatible with the truncated data set, we define the ideal string to be that string for which a weighted average of the density is minimum. We prove that this ideal string must have a finite number of degrees of freedom and hence, that it is made up by a finite number of concentrated point masses. By specializing the optimality criterion, we can also show that the Krein string is an ideal string. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1978
Accession Number
ADA056175

Entities

People

  • Victor Barcilon

Organizations

  • University of Chicago

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Calculus
  • Calculus Of Variations
  • Computer Programming
  • Convection
  • Convex Programming
  • Data Sets
  • Equations
  • Flow
  • Frequency
  • Gravity
  • Gravity Anomalies
  • Inverse Problems
  • New York
  • Security
  • Spectra
  • Turbulent Flow

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Calculus or Mathematical Analysis
  • Structural Dynamics.