IN-PLANE FREE VIBRATION ANALYSIS OF A SCIMITAR-TYPE ROTATING CURVED BEAM USING THE ADOMIAN MODIFIED DECOMPOSITION METHOD
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Date
2020
Authors
Adair, Desmond
Jaeger, Martin
Journal Title
Journal ISSN
Volume Title
Publisher
Mathematical and Computational Applications
Abstract
Free in-plane vibrations of a scimitar-type nonprismatic rotating curved beam, with a
variable cross-section and increasing sweep along the leading edge, are calculated using an innovative,
efficient and accurate solver called the Adomian modified decomposition method (AMDM).
The equation of motion includes the axial force resulting from centrifugal stiffening, and the boundary
conditions imposed are those of a cantilever beam, i.e., clamped-free and simple-free. The AMDM
allows the governing differential equation to become a recursive algebraic equation suitable for
symbolic computation, and, after additional simple mathematical operations, the natural frequencies
and corresponding closed-form series solution of the mode shapes are obtained simultaneously.
Two main advantages of the application of the AMDM are its fast convergence rate to a solution and its
high degree of accuracy. The design shape parameters of the beam, such as transitioning from a straight
beam pattern to a curved beam pattern, are investigated. The accuracy of the model is investigated
using previously reported investigations and using an innovative error analysis procedure.
Description
Keywords
Type of access: Open Access, non-prismatic beam, Adomian modified decomposition method, rotation, curved beam, error analysis
Citation
Adair, D., & Jaeger, M. (2020). In-Plane Free Vibration Analysis of a Scimitar-Type Rotating Curved Beam Using the Adomian Modified Decomposition Method. Mathematical and Computational Applications, 25(4), 68. https://doi.org/10.3390/mca25040068