A power series solution for rotating nonuniform Euler–Bernoulli cantilever beams

Desmond Adair, Martin Jaeger

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


A systematic procedure is developed for studying the dynamic response of a rotating nonuniform Euler–Bernoulli beam with an elastically restrained root. To find the solution, a novel approach is used in that the fourth-order differential equation describing the vibration problem is first written as a first-order matrix differential equation, which is then solved using the power series method. The method can be used to obtain an approximate solution of vibration problems for nonuniform Euler–Bernoulli beams. Specifically, numerical examples are presented here to demonstrate the usefulness of the method in frequency analysis of nonuniform Euler–Bernoulli clamped-free cantilever beams. Results for mode shapes and frequency parameters were found to be in satisfactory agreement with previously published results. The effects of tapering, both equal and unequal, were investigated for both a cantilever wedge and cantilever cone.

Original languageEnglish
Pages (from-to)3855-3864
Number of pages10
JournalJVC/Journal of Vibration and Control
Issue number17
Publication statusPublished - Sep 1 2018


  • cantilever
  • nonuniform Euler–Bernoulli beam
  • Power series method
  • rotating beam

ASJC Scopus subject areas

  • Materials Science(all)
  • Automotive Engineering
  • Aerospace Engineering
  • Mechanics of Materials
  • Mechanical Engineering

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