A high-performance method of vibration analysis for large-scale systems with local strong nonlinearity (Dimension reduction method using new type of complex modal analysis)
A rational dimension reduction method based on a new type of complex modal analysis is developed in order to accurately analyze nonlinear vibrations generated in large-scale structures with local strong nonlinearity, non-proportional damping and asymmetric matrix at low computational cost. In the pr...
| Main Authors: | , , |
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| Format: | Article |
| Language: | Japanese |
| Published: |
The Japan Society of Mechanical Engineers
2021-12-01
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| Series: | Nihon Kikai Gakkai ronbunshu |
| Subjects: | |
| Online Access: | https://www.jstage.jst.go.jp/article/transjsme/87/904/87_21-00210/_pdf/-char/en |
| _version_ | 1797989092301996032 |
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| author | Taiki SUMIKAWA Hiroki MORI Takahiro KONDOU |
| author_facet | Taiki SUMIKAWA Hiroki MORI Takahiro KONDOU |
| author_sort | Taiki SUMIKAWA |
| collection | DOAJ |
| description | A rational dimension reduction method based on a new type of complex modal analysis is developed in order to accurately analyze nonlinear vibrations generated in large-scale structures with local strong nonlinearity, non-proportional damping and asymmetric matrix at low computational cost. In the proposed method, first, the linear state variables are transformed into modal coordinates using complex constrained modes obtained by fixing nonlinear state variables. Next, a reduced model is derived by selecting a small number of modal coordinates that have a significant effect on the computational accuracy of the solution, and coupling them with the nonlinear state variables expressed in physical coordinates. In that process, the remaining modal coordinates that have little effect on the computational accuracy are appropriately approximated and integrated into the equations of motion for nonlinear state variables as correction terms. Furthermore, by using a method of estimating the effect of higher-order modes from lower-order modes, the computation of higher-order eigenpairs becomes unnecessary. From the reduced model constructed by these procedures, periodic solutions and their stability, quasi-periodic solutions and chaos can be computed with a very high accuracy and at a high computational speed. |
| first_indexed | 2024-04-11T08:13:39Z |
| format | Article |
| id | doaj.art-54e281c23f244b23ade1771b8cb6e51d |
| institution | Directory Open Access Journal |
| issn | 2187-9761 |
| language | Japanese |
| last_indexed | 2024-04-11T08:13:39Z |
| publishDate | 2021-12-01 |
| publisher | The Japan Society of Mechanical Engineers |
| record_format | Article |
| series | Nihon Kikai Gakkai ronbunshu |
| spelling | doaj.art-54e281c23f244b23ade1771b8cb6e51d2022-12-22T04:35:14ZjpnThe Japan Society of Mechanical EngineersNihon Kikai Gakkai ronbunshu2187-97612021-12-018790421-0021021-0021010.1299/transjsme.21-00210transjsmeA high-performance method of vibration analysis for large-scale systems with local strong nonlinearity (Dimension reduction method using new type of complex modal analysis)Taiki SUMIKAWA0Hiroki MORI1Takahiro KONDOU2Department of Mechanical Engineering, Kyushu UniversityDepartment of Mechanical Engineering, Faculty of Engineering, Kyushu UniversityKyushu Polytechnic CollegeA rational dimension reduction method based on a new type of complex modal analysis is developed in order to accurately analyze nonlinear vibrations generated in large-scale structures with local strong nonlinearity, non-proportional damping and asymmetric matrix at low computational cost. In the proposed method, first, the linear state variables are transformed into modal coordinates using complex constrained modes obtained by fixing nonlinear state variables. Next, a reduced model is derived by selecting a small number of modal coordinates that have a significant effect on the computational accuracy of the solution, and coupling them with the nonlinear state variables expressed in physical coordinates. In that process, the remaining modal coordinates that have little effect on the computational accuracy are appropriately approximated and integrated into the equations of motion for nonlinear state variables as correction terms. Furthermore, by using a method of estimating the effect of higher-order modes from lower-order modes, the computation of higher-order eigenpairs becomes unnecessary. From the reduced model constructed by these procedures, periodic solutions and their stability, quasi-periodic solutions and chaos can be computed with a very high accuracy and at a high computational speed.https://www.jstage.jst.go.jp/article/transjsme/87/904/87_21-00210/_pdf/-char/ennonlinear vibrationstabilitymethod of vibration analysisdimension reduction methodcomplex modal analysisnon-proportionally damped systemasymmetric matrix system |
| spellingShingle | Taiki SUMIKAWA Hiroki MORI Takahiro KONDOU A high-performance method of vibration analysis for large-scale systems with local strong nonlinearity (Dimension reduction method using new type of complex modal analysis) Nihon Kikai Gakkai ronbunshu nonlinear vibration stability method of vibration analysis dimension reduction method complex modal analysis non-proportionally damped system asymmetric matrix system |
| title | A high-performance method of vibration analysis for large-scale systems with local strong nonlinearity (Dimension reduction method using new type of complex modal analysis) |
| title_full | A high-performance method of vibration analysis for large-scale systems with local strong nonlinearity (Dimension reduction method using new type of complex modal analysis) |
| title_fullStr | A high-performance method of vibration analysis for large-scale systems with local strong nonlinearity (Dimension reduction method using new type of complex modal analysis) |
| title_full_unstemmed | A high-performance method of vibration analysis for large-scale systems with local strong nonlinearity (Dimension reduction method using new type of complex modal analysis) |
| title_short | A high-performance method of vibration analysis for large-scale systems with local strong nonlinearity (Dimension reduction method using new type of complex modal analysis) |
| title_sort | high performance method of vibration analysis for large scale systems with local strong nonlinearity dimension reduction method using new type of complex modal analysis |
| topic | nonlinear vibration stability method of vibration analysis dimension reduction method complex modal analysis non-proportionally damped system asymmetric matrix system |
| url | https://www.jstage.jst.go.jp/article/transjsme/87/904/87_21-00210/_pdf/-char/en |
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