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Extended Wittrick–Williams algorithm for eigenvalue solution of stochastic dynamic stiffness method

Xiang Liu, Xiao Liu, Sondipon Adhikari, Shengwen Yin

Mechanical Systems and Signal Processing, Volume: 166, Start page: 108354

Swansea University Author: Sondipon Adhikari

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DOI (Published version): 10.1016/j.ymssp.2021.108354

Abstract

This paper proposes an efficient and reliable eigenvalue solution technique for analytical stochastic dynamic stiffness (SDS) formulations of beam built-up structures with parametric uncertainties. The SDS formulations are developed based on frequency-dependent shape functions in conjunction with bo...

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Published in: Mechanical Systems and Signal Processing
ISSN: 0888-3270
Published: Elsevier BV 2022
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URI: https://cronfa.swan.ac.uk/Record/cronfa58122
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spelling 2021-10-25T11:31:38.4964902 v2 58122 2021-09-28 Extended Wittrick–Williams algorithm for eigenvalue solution of stochastic dynamic stiffness method 4ea84d67c4e414f5ccbd7593a40f04d3 Sondipon Adhikari Sondipon Adhikari true false 2021-09-28 FGSEN This paper proposes an efficient and reliable eigenvalue solution technique for analytical stochastic dynamic stiffness (SDS) formulations of beam built-up structures with parametric uncertainties. The SDS formulations are developed based on frequency-dependent shape functions in conjunction with both random-variable and random-field structural parameters. The overall numerical framework is aimed towards representing the broadband dynamics of structures using very few degrees of freedom. This paper proposes a novel approach combining the Wittrick–Williams(WW) algorithm, the Newton iteration method and numerical perturbation method to extract eigensolutions from SDS formulations. First, the eigenvalues and eigenvectors of the deterministic DS formulations are computed by the WW algorithm and the corresponding mode finding technique, which are used as the initial solution. Then, a numerical perturbation technique based on the inverse iteration and homotopy method is proposed to update the eigenvectors and eigenvalues. The robustness and efficiency of the proposed method are guaranteed through several technique arrangements. Through numerical examples, the proposed method is demonstrated to be robust within the whole frequency range. This method provides an efficient and reliable tool for stochastic analysis of eigenvalue problems relevant to free vibration and buckling analysis of built-up structures. Journal Article Mechanical Systems and Signal Processing 166 108354 Elsevier BV 0888-3270 Stochastic eigenvalue solution, Stochastic dynamic stiffness method, Wittrick–Williams algorithm, Numerical perturbation method, Random field, Karhunen–Loève expansion 1 3 2022 2022-03-01 10.1016/j.ymssp.2021.108354 COLLEGE NANME Science and Engineering - Faculty COLLEGE CODE FGSEN Swansea University 2021-10-25T11:31:38.4964902 2021-09-28T10:16:02.9562704 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised Xiang Liu 1 Xiao Liu 2 Sondipon Adhikari 3 Shengwen Yin 4 58122__21048__f318e51a679c48ea80b3c114eb14e80c.pdf 58122.pdf 2021-09-29T08:59:48.9816236 Output 1750990 application/pdf Accepted Manuscript true 2022-09-21T00:00:00.0000000 ©2021 All rights reserved. All article content, except where otherwise noted, is licensed under a Creative Commons Attribution Non-Commercial No Derivatives License (CC-BY-NC-ND) true eng https://creativecommons.org/licenses/by-nc-nd/4.0/
title Extended Wittrick–Williams algorithm for eigenvalue solution of stochastic dynamic stiffness method
spellingShingle Extended Wittrick–Williams algorithm for eigenvalue solution of stochastic dynamic stiffness method
Sondipon Adhikari
title_short Extended Wittrick–Williams algorithm for eigenvalue solution of stochastic dynamic stiffness method
title_full Extended Wittrick–Williams algorithm for eigenvalue solution of stochastic dynamic stiffness method
title_fullStr Extended Wittrick–Williams algorithm for eigenvalue solution of stochastic dynamic stiffness method
title_full_unstemmed Extended Wittrick–Williams algorithm for eigenvalue solution of stochastic dynamic stiffness method
title_sort Extended Wittrick–Williams algorithm for eigenvalue solution of stochastic dynamic stiffness method
author_id_str_mv 4ea84d67c4e414f5ccbd7593a40f04d3
author_id_fullname_str_mv 4ea84d67c4e414f5ccbd7593a40f04d3_***_Sondipon Adhikari
author Sondipon Adhikari
author2 Xiang Liu
Xiao Liu
Sondipon Adhikari
Shengwen Yin
format Journal article
container_title Mechanical Systems and Signal Processing
container_volume 166
container_start_page 108354
publishDate 2022
institution Swansea University
issn 0888-3270
doi_str_mv 10.1016/j.ymssp.2021.108354
publisher Elsevier BV
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Engineering and Applied Sciences - Uncategorised{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Engineering and Applied Sciences - Uncategorised
document_store_str 1
active_str 0
description This paper proposes an efficient and reliable eigenvalue solution technique for analytical stochastic dynamic stiffness (SDS) formulations of beam built-up structures with parametric uncertainties. The SDS formulations are developed based on frequency-dependent shape functions in conjunction with both random-variable and random-field structural parameters. The overall numerical framework is aimed towards representing the broadband dynamics of structures using very few degrees of freedom. This paper proposes a novel approach combining the Wittrick–Williams(WW) algorithm, the Newton iteration method and numerical perturbation method to extract eigensolutions from SDS formulations. First, the eigenvalues and eigenvectors of the deterministic DS formulations are computed by the WW algorithm and the corresponding mode finding technique, which are used as the initial solution. Then, a numerical perturbation technique based on the inverse iteration and homotopy method is proposed to update the eigenvectors and eigenvalues. The robustness and efficiency of the proposed method are guaranteed through several technique arrangements. Through numerical examples, the proposed method is demonstrated to be robust within the whole frequency range. This method provides an efficient and reliable tool for stochastic analysis of eigenvalue problems relevant to free vibration and buckling analysis of built-up structures.
published_date 2022-03-01T04:14:23Z
_version_ 1763753972266434560
score 11.037056

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