Eigenpath Following for Systems with Symmetric Complex-Valued Stiffness Matrices
A vibration analysis of a structure with joints is performed. The simulation is conducted with finite element software capable of performing a numeric modal analysis with hysteretic damping assumption. The joints are modeled with thin layer elements, representing dissipation and stiffness of the joi...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.3233/SAV-2010-0535 |
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| _version_ | 1832567033980518400 |
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| author | U. Miller S. Bograd A. Schmidt L. Gaul |
| author_facet | U. Miller S. Bograd A. Schmidt L. Gaul |
| author_sort | U. Miller |
| collection | DOAJ |
| description | A vibration analysis of a structure with joints is performed. The simulation is conducted with finite element software capable of performing a numeric modal analysis with hysteretic damping assumption. The joints are modeled with thin layer elements, representing dissipation and stiffness of the joints. The matrices describing the system consist of the mass, as well as real and complex-valued stiffness matrices. If the eigenvalues of this system are found in one step, due to the mode crossing occurring for the closely spaced modes, it is difficult and time consuming to assign calculated modal damping factors to the corresponding undamped eigenvalues. In order to avoid this problem, an eigenvalue following method is used. The outcome of the solution is the graphical presentation of continuous eigenvalue paths, showing the change in the eigenvalues from the undamped to the fully damped case. For every undamped eigenvalue exists its equivalent eigenfrequency and damping factor that can be used for further numerical analysis. |
| format | Article |
| id | doaj-art-4c4600e4f5df4056a31f2426021cff44 |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-4c4600e4f5df4056a31f2426021cff442025-02-03T01:02:31ZengWileyShock and Vibration1070-96221875-92032010-01-01174-539740510.3233/SAV-2010-0535Eigenpath Following for Systems with Symmetric Complex-Valued Stiffness MatricesU. Miller0S. Bograd1A. Schmidt2L. Gaul3Institute of Applied and Experimental Mechanics, University of Stuttgart, Pfaffenwaldring 9, 70550 Stuttgart, GermanyInstitute of Applied and Experimental Mechanics, University of Stuttgart, Pfaffenwaldring 9, 70550 Stuttgart, GermanyInstitute of Applied and Experimental Mechanics, University of Stuttgart, Pfaffenwaldring 9, 70550 Stuttgart, GermanyInstitute of Applied and Experimental Mechanics, University of Stuttgart, Pfaffenwaldring 9, 70550 Stuttgart, GermanyA vibration analysis of a structure with joints is performed. The simulation is conducted with finite element software capable of performing a numeric modal analysis with hysteretic damping assumption. The joints are modeled with thin layer elements, representing dissipation and stiffness of the joints. The matrices describing the system consist of the mass, as well as real and complex-valued stiffness matrices. If the eigenvalues of this system are found in one step, due to the mode crossing occurring for the closely spaced modes, it is difficult and time consuming to assign calculated modal damping factors to the corresponding undamped eigenvalues. In order to avoid this problem, an eigenvalue following method is used. The outcome of the solution is the graphical presentation of continuous eigenvalue paths, showing the change in the eigenvalues from the undamped to the fully damped case. For every undamped eigenvalue exists its equivalent eigenfrequency and damping factor that can be used for further numerical analysis.http://dx.doi.org/10.3233/SAV-2010-0535 |
| spellingShingle | U. Miller S. Bograd A. Schmidt L. Gaul Eigenpath Following for Systems with Symmetric Complex-Valued Stiffness Matrices Shock and Vibration |
| title | Eigenpath Following for Systems with Symmetric Complex-Valued Stiffness Matrices |
| title_full | Eigenpath Following for Systems with Symmetric Complex-Valued Stiffness Matrices |
| title_fullStr | Eigenpath Following for Systems with Symmetric Complex-Valued Stiffness Matrices |
| title_full_unstemmed | Eigenpath Following for Systems with Symmetric Complex-Valued Stiffness Matrices |
| title_short | Eigenpath Following for Systems with Symmetric Complex-Valued Stiffness Matrices |
| title_sort | eigenpath following for systems with symmetric complex valued stiffness matrices |
| url | http://dx.doi.org/10.3233/SAV-2010-0535 |
| work_keys_str_mv | AT umiller eigenpathfollowingforsystemswithsymmetriccomplexvaluedstiffnessmatrices AT sbograd eigenpathfollowingforsystemswithsymmetriccomplexvaluedstiffnessmatrices AT aschmidt eigenpathfollowingforsystemswithsymmetriccomplexvaluedstiffnessmatrices AT lgaul eigenpathfollowingforsystemswithsymmetriccomplexvaluedstiffnessmatrices |