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Vibration Analysis of Rotating Tapered Beams

Dominic R. Jackson
S. O. Oyadiji

2005 Wolfram Technology Conference
Conference location

Champaign IL

Mathematica is used symbolically to derive the governing differential equations of motion of a rotating tapered Euler-Bernoulli beam in free vibration by Hamiltonís principle and solved by the Frobenius power series method, respectively. The beam has a symmetric cross section and a root offset from the axis of rotation. The exact non-dimensional natural frequencies of vibration are evaluated for a few boundary conditions using simple Mathematica routines. The effect of root offset variation and taper ratio on the natural frequencies of vibration are also investigated. Due to the very few publications available on the subject, a finite element method is also used to validate the results obtained using Mathematica and the agreement is excellent. The results demonstrate the reliability and the ease with which symbolic and numerical operations are carried out in Mathematica. The paper also serves as a building block for the use of Mathematica in vibration analysis of rotating beams, plates, and more complicated engineering structures.

*Engineering > Architecture