Identification of Nonlinear Modal Interactions in a Beam-Mass-Spring-Damper System based on Mono-Frequency Vibration Response
In this paper, nonlinear modal interactions caused by one-to-three internal resonance in a beam-mass-spring-damper system are investigated based on nonlinear system identification. For this purpose, the equations governing the transverse vibrations of the beam and mass are analyzed via the multiple...
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| Format: | Article |
| Language: | fas |
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Isfahan University of Technology
2019-08-01
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| Series: | Ravish/hā-yi ̒adadī dar Muhandisī |
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| Online Access: | http://jcme.iut.ac.ir/article-1-659-en.html |
| _version_ | 1818643797131657216 |
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| author | M. H. Sadeghi S. Lotfan |
| author_facet | M. H. Sadeghi S. Lotfan |
| author_sort | M. H. Sadeghi |
| collection | DOAJ |
| description | In this paper, nonlinear modal interactions caused by one-to-three internal resonance in a beam-mass-spring-damper system are investigated based on nonlinear system identification. For this purpose, the equations governing the transverse vibrations of the beam and mass are analyzed via the multiple scale method and the vibration response of the system under primary resonance is extracted. Then, the frequency behavior of the vibration response is studied by Fourier and Morlet wavelet transforms. In order to perform the nonparametric identification of the time response, mono-frequency intrinsic mode functions are derived by the advanced empirical mode decomposition. In this approach, masking signals are utilized in order to avoid mode mixing caused by modal interaction. After analyzing the frequency behavior of each mode function, slow flow dynamics of the system is established and intrinsic modal oscillators for reconstructing the corresponding intrinsic mode are extracted. Finally, by analyzing the beating phenomenon in a simple one-degree-of-freedom system, it is shown that the internal resonance causes beating only under the circumstance that the slope of the logarithmic amplitude of oscillator force is nonzero. The results, therefore, show that depending on the periodic, pseudo-periodic, and chaotic behavior of the response, modal interactions might be stationary or non-stationary. Moreover, the chaotic behavior occurs mostly in the vibration mode excited by the internal resonance mechanism |
| first_indexed | 2024-12-17T00:04:39Z |
| format | Article |
| id | doaj.art-0372749d3cd744a786892d7d9838c02f |
| institution | Directory Open Access Journal |
| issn | 2228-7698 2423-5741 |
| language | fas |
| last_indexed | 2024-12-17T00:04:39Z |
| publishDate | 2019-08-01 |
| publisher | Isfahan University of Technology |
| record_format | Article |
| series | Ravish/hā-yi ̒adadī dar Muhandisī |
| spelling | doaj.art-0372749d3cd744a786892d7d9838c02f2022-12-21T22:10:58ZfasIsfahan University of TechnologyRavish/hā-yi ̒adadī dar Muhandisī2228-76982423-57412019-08-013811936Identification of Nonlinear Modal Interactions in a Beam-Mass-Spring-Damper System based on Mono-Frequency Vibration ResponseM. H. Sadeghi0S. Lotfan1 Department of Mechanical Engineering, University of Tabriz, Tabriz, Iran. Department of Mechanical Engineering, University of Tabriz, Tabriz, Iran. In this paper, nonlinear modal interactions caused by one-to-three internal resonance in a beam-mass-spring-damper system are investigated based on nonlinear system identification. For this purpose, the equations governing the transverse vibrations of the beam and mass are analyzed via the multiple scale method and the vibration response of the system under primary resonance is extracted. Then, the frequency behavior of the vibration response is studied by Fourier and Morlet wavelet transforms. In order to perform the nonparametric identification of the time response, mono-frequency intrinsic mode functions are derived by the advanced empirical mode decomposition. In this approach, masking signals are utilized in order to avoid mode mixing caused by modal interaction. After analyzing the frequency behavior of each mode function, slow flow dynamics of the system is established and intrinsic modal oscillators for reconstructing the corresponding intrinsic mode are extracted. Finally, by analyzing the beating phenomenon in a simple one-degree-of-freedom system, it is shown that the internal resonance causes beating only under the circumstance that the slope of the logarithmic amplitude of oscillator force is nonzero. The results, therefore, show that depending on the periodic, pseudo-periodic, and chaotic behavior of the response, modal interactions might be stationary or non-stationary. Moreover, the chaotic behavior occurs mostly in the vibration mode excited by the internal resonance mechanismhttp://jcme.iut.ac.ir/article-1-659-en.htmlBeam-mass-spring-damper systemNonlinear modal interactionsNonlinear system identificationAdvanced empirical mode decomposition |
| spellingShingle | M. H. Sadeghi S. Lotfan Identification of Nonlinear Modal Interactions in a Beam-Mass-Spring-Damper System based on Mono-Frequency Vibration Response Ravish/hā-yi ̒adadī dar Muhandisī Beam-mass-spring-damper system Nonlinear modal interactions Nonlinear system identification Advanced empirical mode decomposition |
| title | Identification of Nonlinear Modal Interactions in a Beam-Mass-Spring-Damper System based on Mono-Frequency Vibration Response |
| title_full | Identification of Nonlinear Modal Interactions in a Beam-Mass-Spring-Damper System based on Mono-Frequency Vibration Response |
| title_fullStr | Identification of Nonlinear Modal Interactions in a Beam-Mass-Spring-Damper System based on Mono-Frequency Vibration Response |
| title_full_unstemmed | Identification of Nonlinear Modal Interactions in a Beam-Mass-Spring-Damper System based on Mono-Frequency Vibration Response |
| title_short | Identification of Nonlinear Modal Interactions in a Beam-Mass-Spring-Damper System based on Mono-Frequency Vibration Response |
| title_sort | identification of nonlinear modal interactions in a beam mass spring damper system based on mono frequency vibration response |
| topic | Beam-mass-spring-damper system Nonlinear modal interactions Nonlinear system identification Advanced empirical mode decomposition |
| url | http://jcme.iut.ac.ir/article-1-659-en.html |
| work_keys_str_mv | AT mhsadeghi identificationofnonlinearmodalinteractionsinabeammassspringdampersystembasedonmonofrequencyvibrationresponse AT slotfan identificationofnonlinearmodalinteractionsinabeammassspringdampersystembasedonmonofrequencyvibrationresponse |