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A power series solution for rotating nonuniform Euler-Bernoulli cantilever beams
journal contribution
posted on 2023-05-19, 13:39 authored by Adair, D, Jaeger, MA 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.
History
Publication title
Journal of Vibration and ControlVolume
24Issue
17Pagination
3855-3864ISSN
1077-5463Department/School
School of EngineeringPublisher
Sage Publications LtdPlace of publication
6 Bonhill Street, London, England, Ec2A 4PuRights statement
Copyright The Author(s) 2017Repository Status
- Restricted