Nonlinear Resonance Analysis of Slender Portal Frames under Base Excitation
The dynamic nonlinear response and stability of slender structures in the main resonance regions are a topic of importance in structural analysis. In complex problems, the determination of the response in the frequency domain indirectly obtained through analyses in time domain can lead to huge compu...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2017/5281237 |
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| _version_ | 1832555842043379712 |
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| author | Luis Fernando Paullo Muñoz Paulo B. Gonçalves Ricardo A. M. Silveira Andréa Silva |
| author_facet | Luis Fernando Paullo Muñoz Paulo B. Gonçalves Ricardo A. M. Silveira Andréa Silva |
| author_sort | Luis Fernando Paullo Muñoz |
| collection | DOAJ |
| description | The dynamic nonlinear response and stability of slender structures in the main resonance regions are a topic of importance in structural analysis. In complex problems, the determination of the response in the frequency domain indirectly obtained through analyses in time domain can lead to huge computational effort in large systems. In nonlinear cases, the response in the frequency domain becomes even more cumbersome because of the possibility of multiple solutions for certain forcing frequencies. Those solutions can be stable and unstable, in particular saddle-node bifurcation at the turning points along the resonance curves. In this work, an incremental technique for direct calculation of the nonlinear response in frequency domain of plane frames subjected to base excitation is proposed. The transformation of equations of motion to the frequency domain is made through the harmonic balance method in conjunction with the Galerkin method. The resulting system of nonlinear equations in terms of the modal amplitudes and forcing frequency is solved by the Newton-Raphson method together with an arc-length procedure to obtain the nonlinear resonance curves. Suitable examples are presented, and the influence of the frame geometric parameters and base motion on the nonlinear resonance curves is investigated. |
| format | Article |
| id | doaj-art-0effc9ae12884fd38d9df8a6cf1e92c8 |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-0effc9ae12884fd38d9df8a6cf1e92c82025-02-03T05:46:55ZengWileyShock and Vibration1070-96221875-92032017-01-01201710.1155/2017/52812375281237Nonlinear Resonance Analysis of Slender Portal Frames under Base ExcitationLuis Fernando Paullo Muñoz0Paulo B. Gonçalves1Ricardo A. M. Silveira2Andréa Silva3Civil Engineering Department, Pontifical Catholic University of Rio de Janeiro, Rio de Janeiro, RJ, BrazilCivil Engineering Department, Pontifical Catholic University of Rio de Janeiro, Rio de Janeiro, RJ, BrazilCivil Engineering Department, Federal University of Ouro Preto, Ouro Preto, MG, BrazilCivil Engineering Department, Federal University of Ouro Preto, Ouro Preto, MG, BrazilThe dynamic nonlinear response and stability of slender structures in the main resonance regions are a topic of importance in structural analysis. In complex problems, the determination of the response in the frequency domain indirectly obtained through analyses in time domain can lead to huge computational effort in large systems. In nonlinear cases, the response in the frequency domain becomes even more cumbersome because of the possibility of multiple solutions for certain forcing frequencies. Those solutions can be stable and unstable, in particular saddle-node bifurcation at the turning points along the resonance curves. In this work, an incremental technique for direct calculation of the nonlinear response in frequency domain of plane frames subjected to base excitation is proposed. The transformation of equations of motion to the frequency domain is made through the harmonic balance method in conjunction with the Galerkin method. The resulting system of nonlinear equations in terms of the modal amplitudes and forcing frequency is solved by the Newton-Raphson method together with an arc-length procedure to obtain the nonlinear resonance curves. Suitable examples are presented, and the influence of the frame geometric parameters and base motion on the nonlinear resonance curves is investigated.http://dx.doi.org/10.1155/2017/5281237 |
| spellingShingle | Luis Fernando Paullo Muñoz Paulo B. Gonçalves Ricardo A. M. Silveira Andréa Silva Nonlinear Resonance Analysis of Slender Portal Frames under Base Excitation Shock and Vibration |
| title | Nonlinear Resonance Analysis of Slender Portal Frames under Base Excitation |
| title_full | Nonlinear Resonance Analysis of Slender Portal Frames under Base Excitation |
| title_fullStr | Nonlinear Resonance Analysis of Slender Portal Frames under Base Excitation |
| title_full_unstemmed | Nonlinear Resonance Analysis of Slender Portal Frames under Base Excitation |
| title_short | Nonlinear Resonance Analysis of Slender Portal Frames under Base Excitation |
| title_sort | nonlinear resonance analysis of slender portal frames under base excitation |
| url | http://dx.doi.org/10.1155/2017/5281237 |
| work_keys_str_mv | AT luisfernandopaullomunoz nonlinearresonanceanalysisofslenderportalframesunderbaseexcitation AT paulobgoncalves nonlinearresonanceanalysisofslenderportalframesunderbaseexcitation AT ricardoamsilveira nonlinearresonanceanalysisofslenderportalframesunderbaseexcitation AT andreasilva nonlinearresonanceanalysisofslenderportalframesunderbaseexcitation |