New theoretical developments on eigenvector derivatives with repeated eigenvalues

Many different methods have been developed since the pioneering works of Mills-Curran (1988) and Dailey (1989) on eigenvector derivatives with repeated eigenvalues. In spite of the increasing mathematical complexities witnessed in many of the newly emerged methods, some underlying fundamental theori...

Full description

Bibliographic Details
Main Authors: Lin, Rongming, Ng, Teng Yong
Other Authors: School of Mechanical and Aerospace Engineering
Format: Journal Article
Language:English
Published: 2021
Subjects:
Online Access:https://hdl.handle.net/10356/151297
_version_ 1826120751175958528
author Lin, Rongming
Ng, Teng Yong
author2 School of Mechanical and Aerospace Engineering
author_facet School of Mechanical and Aerospace Engineering
Lin, Rongming
Ng, Teng Yong
author_sort Lin, Rongming
collection NTU
description Many different methods have been developed since the pioneering works of Mills-Curran (1988) and Dailey (1989) on eigenvector derivatives with repeated eigenvalues. In spite of the increasing mathematical complexities witnessed in many of the newly emerged methods, some underlying fundamental theories governing the eigenvector derivatives have neither been much discussed, nor fully established to date. The present approach seeks to fill such an outstanding theoretical gap and to lay down the necessary theoretical foundation on which existing methods can be mathematically unified and further improved in numerical accuracy and computational efficiency. The particular solutions of eigenvector derivatives generally required have been derived in terms of modal properties, thereby avoiding the computationally expensive and potentially erroneous procedure of solving a set of algebraic equations of system dimension. The contributions of higher unavailable modes have been theoretically derived, enhancing the practical applicability of the proposed method to the general case where only partial eigensolutions are made. To avoid degeneration of eigenvector space in the case of repeated eigenvalues, a concept of global design variable is developed in which all intended multivariate design modifications are grouped into a single global variable to which eigenvector derivatives are derived, rendering real major applications of the proposed method to the predictions of structural design modifications. A discrete parameter model of a turbine bladed disk assembly, which is known to have many pairs of repeated eigenvalues due to its cyclic symmetry, as well as a finite element model of a cantilevered beam with large DOFs have been employed. Numerical results have demonstrated the accuracy and the practical applicability of the proposed new theoretical developments, as well as the proposed new method.
first_indexed 2024-10-01T05:21:53Z
format Journal Article
id ntu-10356/151297
institution Nanyang Technological University
language English
last_indexed 2024-10-01T05:21:53Z
publishDate 2021
record_format dspace
spelling ntu-10356/1512972021-07-06T01:27:14Z New theoretical developments on eigenvector derivatives with repeated eigenvalues Lin, Rongming Ng, Teng Yong School of Mechanical and Aerospace Engineering Engineering::Mechanical engineering Theoretical Development Eigenvector Derivatives Many different methods have been developed since the pioneering works of Mills-Curran (1988) and Dailey (1989) on eigenvector derivatives with repeated eigenvalues. In spite of the increasing mathematical complexities witnessed in many of the newly emerged methods, some underlying fundamental theories governing the eigenvector derivatives have neither been much discussed, nor fully established to date. The present approach seeks to fill such an outstanding theoretical gap and to lay down the necessary theoretical foundation on which existing methods can be mathematically unified and further improved in numerical accuracy and computational efficiency. The particular solutions of eigenvector derivatives generally required have been derived in terms of modal properties, thereby avoiding the computationally expensive and potentially erroneous procedure of solving a set of algebraic equations of system dimension. The contributions of higher unavailable modes have been theoretically derived, enhancing the practical applicability of the proposed method to the general case where only partial eigensolutions are made. To avoid degeneration of eigenvector space in the case of repeated eigenvalues, a concept of global design variable is developed in which all intended multivariate design modifications are grouped into a single global variable to which eigenvector derivatives are derived, rendering real major applications of the proposed method to the predictions of structural design modifications. A discrete parameter model of a turbine bladed disk assembly, which is known to have many pairs of repeated eigenvalues due to its cyclic symmetry, as well as a finite element model of a cantilevered beam with large DOFs have been employed. Numerical results have demonstrated the accuracy and the practical applicability of the proposed new theoretical developments, as well as the proposed new method. 2021-07-06T01:27:13Z 2021-07-06T01:27:13Z 2019 Journal Article Lin, R. & Ng, T. Y. (2019). New theoretical developments on eigenvector derivatives with repeated eigenvalues. Mechanical Systems and Signal Processing, 129, 677-693. https://dx.doi.org/10.1016/j.ymssp.2019.04.037 0888-3270 https://hdl.handle.net/10356/151297 10.1016/j.ymssp.2019.04.037 2-s2.0-85065073002 129 677 693 en Mechanical Systems and Signal Processing © 2019 Elsevier Ltd. All rights reserved.
spellingShingle Engineering::Mechanical engineering
Theoretical Development
Eigenvector Derivatives
Lin, Rongming
Ng, Teng Yong
New theoretical developments on eigenvector derivatives with repeated eigenvalues
title New theoretical developments on eigenvector derivatives with repeated eigenvalues
title_full New theoretical developments on eigenvector derivatives with repeated eigenvalues
title_fullStr New theoretical developments on eigenvector derivatives with repeated eigenvalues
title_full_unstemmed New theoretical developments on eigenvector derivatives with repeated eigenvalues
title_short New theoretical developments on eigenvector derivatives with repeated eigenvalues
title_sort new theoretical developments on eigenvector derivatives with repeated eigenvalues
topic Engineering::Mechanical engineering
Theoretical Development
Eigenvector Derivatives
url https://hdl.handle.net/10356/151297
work_keys_str_mv AT linrongming newtheoreticaldevelopmentsoneigenvectorderivativeswithrepeatedeigenvalues
AT ngtengyong newtheoreticaldevelopmentsoneigenvectorderivativeswithrepeatedeigenvalues