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Abstract

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

Item Type:	Article
Authors/Creators:	Adair, D and Jaeger, M
Keywords:	Power series method, rotating beam, nonuniform Euler–Bernoulli beam, cantilever
Journal or Publication Title:	Journal of Vibration and Control
Publisher:	Sage Publications Ltd
ISSN:	1077-5463
DOI / ID Number:	10.1177/1077546317714183
Copyright Information:	Copyright The Author(s) 2017
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