Discrete singular convolution-polynomial chaos expansion method for free vibration analysis of non-uniform uncertain beams
Discrete singular convolution-polynomial chaos expansion method for free vibration analysis of non-uniform uncertain beams
This article enhances the discrete singular convolution method for free vibration analysis of non-uniform thin beams with variability in their geometrical and material properties such as thickness, specific volume (inverse of density) and Young’s modulus. The discrete singular convolution method solves the differential equation of motion of a structure with a high accuracy using a small number of discretisation points. The method uses polynomial chaos expansion to express these variabilities simulating uncertainty in a closed form. Non-uniformity is locally provided by changing the cross section and Young’s modulus of the beam along its length. In this context, firstly natural frequencies of deterministic uniform and non-uniform beams are predicted via the discrete singular convolution. These results are compared with finite element calculations and analytical solutions (if available) for the purpose of verification. Next, the uncertainty of the beam because of geometrical and material variabilities is modelled in a global manner by polynomial chaos expansion to predict probability distribution functions of the natural frequencies. Monte Carlo simulations are then performed for validation purpose. Results show that the proposed algorithm of the discrete singular convolution with polynomial chaos expansion is very accurate and also efficient, regarding computation cost, in handling non-uniform beams having material and geometrical variabilities. Therefore, it promises that it can be reliably applied to more complex structures having uncertain parameters.
Non-uniform beam, Polynomial Chaos Expansion, discrete singular convolution, natural frequency, uncertainty
1165-1175
Seçgin, Abdullah
3f337aff-c78b-45c2-8a7a-2511991cfe15
Kara, Murat
f2b0b835-a0b7-43b1-ad7f-e081bc909488
Ferguson, Neil
8cb67e30-48e2-491c-9390-d444fa786ac8
1 May 2022
Seçgin, Abdullah
3f337aff-c78b-45c2-8a7a-2511991cfe15
Kara, Murat
f2b0b835-a0b7-43b1-ad7f-e081bc909488
Ferguson, Neil
8cb67e30-48e2-491c-9390-d444fa786ac8
Seçgin, Abdullah, Kara, Murat and Ferguson, Neil
(2022)
Discrete singular convolution-polynomial chaos expansion method for free vibration analysis of non-uniform uncertain beams.
Journal of Vibration and Control, 28 (9-10), .
(doi:10.1177/1077546320988190).
Abstract
This article enhances the discrete singular convolution method for free vibration analysis of non-uniform thin beams with variability in their geometrical and material properties such as thickness, specific volume (inverse of density) and Young’s modulus. The discrete singular convolution method solves the differential equation of motion of a structure with a high accuracy using a small number of discretisation points. The method uses polynomial chaos expansion to express these variabilities simulating uncertainty in a closed form. Non-uniformity is locally provided by changing the cross section and Young’s modulus of the beam along its length. In this context, firstly natural frequencies of deterministic uniform and non-uniform beams are predicted via the discrete singular convolution. These results are compared with finite element calculations and analytical solutions (if available) for the purpose of verification. Next, the uncertainty of the beam because of geometrical and material variabilities is modelled in a global manner by polynomial chaos expansion to predict probability distribution functions of the natural frequencies. Monte Carlo simulations are then performed for validation purpose. Results show that the proposed algorithm of the discrete singular convolution with polynomial chaos expansion is very accurate and also efficient, regarding computation cost, in handling non-uniform beams having material and geometrical variabilities. Therefore, it promises that it can be reliably applied to more complex structures having uncertain parameters.
Text
Paper accepted December 2020
- Accepted Manuscript
More information
Submitted date: 21 October 2020
Accepted/In Press date: 22 December 2020
e-pub ahead of print date: 8 February 2021
Published date: 1 May 2022
Additional Information:
Funding Information:
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This study is supported by “The Scientific and Technological Research Council of Turkey, TUBITAK” in the frame of TUBITAK 2219 programme.
Publisher Copyright:
© The Author(s) 2021.
Keywords:
Non-uniform beam, Polynomial Chaos Expansion, discrete singular convolution, natural frequency, uncertainty
Identifiers
Local EPrints ID: 446345
URI: http://eprints.soton.ac.uk/id/eprint/446345
ISSN: 1077-5463
PURE UUID: 70fce9ed-ee18-4189-9ee3-c76acfba6559
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Date deposited: 05 Feb 2021 17:30
Last modified: 17 Mar 2024 02:32
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Author:
Abdullah Seçgin
Author:
Murat Kara
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