Singular value decomposition of dynamic response of structures
Introduction. This paper presents the results of the decomposition of the synthesized free damped vibrations of a linear cantilever dynamic model into elementary components using singular value decomposition of the displacement matrix.Materials and methods. The well-known representation of a rectang...
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Moscow State University of Civil Engineering (MGSU)
2023-12-01
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| Online Access: | https://www.vestnikmgsu.ru/jour/article/view/128 |
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| author | Yu. A. Kolotovichev |
| author_facet | Yu. A. Kolotovichev |
| author_sort | Yu. A. Kolotovichev |
| collection | DOAJ |
| description | Introduction. This paper presents the results of the decomposition of the synthesized free damped vibrations of a linear cantilever dynamic model into elementary components using singular value decomposition of the displacement matrix.Materials and methods. The well-known representation of a rectangular matrix in the form of a product of three matrix multipliers, called singular value decomposition (SVD), was used in the study.Results. Representing the dynamic response of a structure in a certain matrix form allows for the results of the singular value decomposition to have a clear physical interpretation: the left singular vectors approximate the eigenvectors, the singular values themselves determine the contribution of individual eigenmodes to the overall dynamic response, and the products of singular values and right singular vectors approximate the modal coordinates of the dynamic system at the time under consideration. Singular value decomposition allows to “automatically” obtain an a priori vector basis based on the external manifestations of the dynamic reaction (displacement, velocity or acceleration of the points of the structure), whereas the eigenvectors traditionally used for these purposes are a posteriori basis based on the study of the internal inertia, stiffness and damping properties.Conclusions. This study confirmed the possibility of using displacement matrix SVD to determine the major dynamic parameters of linear dynamic systems: eigenmodes, eigenfrequencies and quantitative damping parameters. All stages of obtaining and subsequent analysis of the dynamic response elementary components are easily automated, which allows to consider SVD as a basis for software development of automatic dynamic monitoring systems of structures under construction and in operation. |
| format | Article |
| id | doaj-art-8d6274948c2c40c99146e269274c7973 |
| institution | Kabale University |
| issn | 1997-0935 2304-6600 |
| language | English |
| publishDate | 2023-12-01 |
| publisher | Moscow State University of Civil Engineering (MGSU) |
| record_format | Article |
| series | Vestnik MGSU |
| spelling | doaj-art-8d6274948c2c40c99146e269274c79732025-01-09T08:22:49ZengMoscow State University of Civil Engineering (MGSU)Vestnik MGSU1997-09352304-66002023-12-0118121880189110.22227/1997-0935.2023.12.1880-189153Singular value decomposition of dynamic response of structuresYu. A. Kolotovichev0Moscow State University of Civil Engineering (National Research University) (MGSU); SODIS LabIntroduction. This paper presents the results of the decomposition of the synthesized free damped vibrations of a linear cantilever dynamic model into elementary components using singular value decomposition of the displacement matrix.Materials and methods. The well-known representation of a rectangular matrix in the form of a product of three matrix multipliers, called singular value decomposition (SVD), was used in the study.Results. Representing the dynamic response of a structure in a certain matrix form allows for the results of the singular value decomposition to have a clear physical interpretation: the left singular vectors approximate the eigenvectors, the singular values themselves determine the contribution of individual eigenmodes to the overall dynamic response, and the products of singular values and right singular vectors approximate the modal coordinates of the dynamic system at the time under consideration. Singular value decomposition allows to “automatically” obtain an a priori vector basis based on the external manifestations of the dynamic reaction (displacement, velocity or acceleration of the points of the structure), whereas the eigenvectors traditionally used for these purposes are a posteriori basis based on the study of the internal inertia, stiffness and damping properties.Conclusions. This study confirmed the possibility of using displacement matrix SVD to determine the major dynamic parameters of linear dynamic systems: eigenmodes, eigenfrequencies and quantitative damping parameters. All stages of obtaining and subsequent analysis of the dynamic response elementary components are easily automated, which allows to consider SVD as a basis for software development of automatic dynamic monitoring systems of structures under construction and in operation.https://www.vestnikmgsu.ru/jour/article/view/128structural dynamicsoperational modal analysissingular value decompositionsvdeigenvectorseigenfrequenciesdampingstructural health monitoringshmdynamic monitoring |
| spellingShingle | Yu. A. Kolotovichev Singular value decomposition of dynamic response of structures Vestnik MGSU structural dynamics operational modal analysis singular value decomposition svd eigenvectors eigenfrequencies damping structural health monitoring shm dynamic monitoring |
| title | Singular value decomposition of dynamic response of structures |
| title_full | Singular value decomposition of dynamic response of structures |
| title_fullStr | Singular value decomposition of dynamic response of structures |
| title_full_unstemmed | Singular value decomposition of dynamic response of structures |
| title_short | Singular value decomposition of dynamic response of structures |
| title_sort | singular value decomposition of dynamic response of structures |
| topic | structural dynamics operational modal analysis singular value decomposition svd eigenvectors eigenfrequencies damping structural health monitoring shm dynamic monitoring |
| url | https://www.vestnikmgsu.ru/jour/article/view/128 |
| work_keys_str_mv | AT yuakolotovichev singularvaluedecompositionofdynamicresponseofstructures |