Vibrational model of a prismatic multilayered tapered cantilever using perturbation analysis

In this work we present a novel semi-analytical model of the vibrational dynamics of a multi-layered tapered prismatic cantilever. The derivation of the model is based on a perturbation expansion of the tapered cantilever's partial differential equations using Euler-Bernoulli beam theory as a s...

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Bibliographic Details
Published in:Journal of sound and vibration 2019-02, Vol.441, p.1-25
Main Authors: Syed, Wajih Umar, Elfadel, Ibrahim (Abe) M.
Format: Article
Language:English
Subjects:
Beam theory (structures)
Cantilever beams
Eigenanalysis
Euler-Bernoulli beams
Eulers equations
Finite element method
Green's function
Mathematical models
Modal analysis
Multilayers
Partial differential equations
Perturbation
Perturbation methods
Tapered cantilever
Vibration analysis
Vibrational model
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Summary:In this work we present a novel semi-analytical model of the vibrational dynamics of a multi-layered tapered prismatic cantilever. The derivation of the model is based on a perturbation expansion of the tapered cantilever's partial differential equations using Euler-Bernoulli beam theory as a starting point. The proposed semi-analytical solution of the model enables a 101-sample modal analysis to run more than 250 × faster when using 20 perturbation components than a computationally efficient commercial FEM solution that uses 101 shell-type finite elements along the beam length and 6 elements along the beam width. In this case, the primary mode model prediction error on resonance frequency is below 0.1% for 20 perturbation components and below 10% for 4 components.
ISSN:0022-460X
1095-8568
DOI:10.1016/j.jsv.2018.10.033