Flexural-Torsional Coupled Vibration of Rotating Beams Using Orthogonal Polynomials

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.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Aerospace and Ocean Engineering

Department dc:contributor.department

Aerospace and Ocean Engineering

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2000

Author dc:creator

• Kim, Yong Y.

Chair dc:contributor.committeechair

• Kapania, Rakesh K.

Committee members dc:contributor.committeemember

• Johnson, Eric R.
• Nikolaidis, Efstratios

• Rotating blade
• Orthogonal polynomials
• Rayleigh-Ritzm method
• Natural frequency
• Felxural-torsional coupled vibration

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-05122000-14040026

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/32616