Title page for ETD etd-05122000-14040026


Type of Document Master's Thesis
Author Kim, Yong Y.
URN etd-05122000-14040026
Title Flexural-Torsional Coupled Vibration of Rotating Beams Using Orthogonal Polynomials
Degree Master of Science
Department Aerospace and Ocean Engineering
Advisory Committee
Advisor Name Title
Kapania, Rakesh K. Committee Chair
Johnson, Eric R. Committee Member
Nikolaidis, Efstratios Committee Member
Keywords
  • Rotating blade
  • Orthogonal polynomials
  • Rayleigh-Ritzm method
  • Natural frequency
  • Felxural-torsional coupled vibration
Date of Defense 2000-05-01
Availability unrestricted
Abstract
Dynamic behavior of flexural-torsional coupled vibration of rotating beams using the Rayleigh-Ritz method with orthogonal polynomials as basis functions is studied. The present work starts from a review of the development and analysis of four basic types of beam theories: the Euler-Bernoulli, Rayleigh, Shear and Timoshenko and goes over to a study of flexural-torsional coupled vibration analysis using basic beam theories. In obtaining natural frequencies, orthogonal polynomials used in the Rayleigh-Ritz method are studied as an efficient way of getting results. The study is also performed for both non-rotating and rotating beams. Orthogonal polynomials and functions studied in the present work are : Legendre, Chebyshev, integrated Legendre, modified Duncan polynomials, the eigenfunctions of a pinned-free uniform beam, and the special trigonometric functions used in conjunction with Hermite cubics. Studied cases are non-rotating and rotating Timoshenko beams, bending-torsion coupled beam with free-free boundary conditions, a cantilever beam, and a rotating cantilever beam. The obtained natural frequencies and mode shapes are compared to those available in various references and results for coupled flexural-torsional vibrations are compared to both previously available references and with those obtained using NASTRAN finite element package.

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