Solution bounds for varying geometry beams

T. J. McDaniel, V. R. Murthy

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


The theory of differential and integral inequalities is applied to obtain upper and lower bounds to the transfer matrix for beams with varying geometry. Various techniques of generating and refining these bounds are investigated. Numerical results indicate that these bounds can be refined to produce numerical agreement of the upper and the lower bound to a given number of significant digits. Proceeding from bounds on the transfer matrix elements a theory is developed for determining upper and lower bounds on the natural frequencies and mode shapes and on the solution state vector for static loading of such beams. This procedure is then extended to the analysis of multispan beams with varying geometry. Numerical results are presented for various configurations.

Original languageEnglish (US)
Pages (from-to)431-448
Number of pages18
JournalJournal of Sound and Vibration
Issue number3
StatePublished - Feb 8 1976
Externally publishedYes

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Acoustics and Ultrasonics


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