Sustained High-Frequency Dynamic Instability of a Nonlinear System of Coupled Oscillators Forced by Single or Repeated Impulses: Theoretical and Experimental Results
This report describes the impulsive dynamics of a system of two coupled oscillators with essential (nonlinearizable) stiffness nonlinearity. The system considered consists of a grounded weakly damped linear oscillator coupled to a lightweight weakly damped oscillating attachment with essential cubic...
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| Format: | Article |
| Language: | en_US |
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ASME International
2015
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| Online Access: | http://hdl.handle.net/1721.1/97929 https://orcid.org/0000-0003-0302-0691 |
| _version_ | 1826188345777061888 |
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| author | Remick, Kevin Vakakis, Alexander McFarland, D. Michael Quinn, D. Dane Sapsis, Themistoklis |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Remick, Kevin Vakakis, Alexander McFarland, D. Michael Quinn, D. Dane Sapsis, Themistoklis |
| author_sort | Remick, Kevin |
| collection | MIT |
| description | This report describes the impulsive dynamics of a system of two coupled oscillators with essential (nonlinearizable) stiffness nonlinearity. The system considered consists of a grounded weakly damped linear oscillator coupled to a lightweight weakly damped oscillating attachment with essential cubic stiffness nonlinearity arising purely from geometry and kinematics. It has been found that under specific impulse excitations the transient damped dynamics of this system tracks a high-frequency impulsive orbit manifold (IOM) in the frequency-energy plane. The IOM extends over finite frequency and energy ranges, consisting of a countable infinity of periodic orbits and an uncountable infinity of quasi-periodic orbits of the underlying Hamiltonian system and being initially at rest and subjected to an impulsive force on the linear oscillator. The damped nonresonant dynamics tracking the IOM then resembles continuous resonance scattering; in effect, quickly transitioning between multiple resonance captures over finite frequency and energy ranges. Dynamic instability arises at bifurcation points along this damped transition, causing bursts in the response of the nonlinear light oscillator, which resemble self-excited resonances. It is shown that for an appropriate parameter design the system remains in a state of sustained high-frequency dynamic instability under the action of repeated impulses. In turn, this sustained instability results in strong energy transfers from the directly excited oscillator to the lightweight nonlinear attachment; a feature that can be employed in energy harvesting applications. The theoretical predictions are confirmed by experimental results. |
| first_indexed | 2024-09-23T07:58:15Z |
| format | Article |
| id | mit-1721.1/97929 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T07:58:15Z |
| publishDate | 2015 |
| publisher | ASME International |
| record_format | dspace |
| spelling | mit-1721.1/979292022-09-30T01:22:27Z Sustained High-Frequency Dynamic Instability of a Nonlinear System of Coupled Oscillators Forced by Single or Repeated Impulses: Theoretical and Experimental Results Remick, Kevin Vakakis, Alexander McFarland, D. Michael Quinn, D. Dane Sapsis, Themistoklis Massachusetts Institute of Technology. Department of Mechanical Engineering Sapsis, Themistoklis This report describes the impulsive dynamics of a system of two coupled oscillators with essential (nonlinearizable) stiffness nonlinearity. The system considered consists of a grounded weakly damped linear oscillator coupled to a lightweight weakly damped oscillating attachment with essential cubic stiffness nonlinearity arising purely from geometry and kinematics. It has been found that under specific impulse excitations the transient damped dynamics of this system tracks a high-frequency impulsive orbit manifold (IOM) in the frequency-energy plane. The IOM extends over finite frequency and energy ranges, consisting of a countable infinity of periodic orbits and an uncountable infinity of quasi-periodic orbits of the underlying Hamiltonian system and being initially at rest and subjected to an impulsive force on the linear oscillator. The damped nonresonant dynamics tracking the IOM then resembles continuous resonance scattering; in effect, quickly transitioning between multiple resonance captures over finite frequency and energy ranges. Dynamic instability arises at bifurcation points along this damped transition, causing bursts in the response of the nonlinear light oscillator, which resemble self-excited resonances. It is shown that for an appropriate parameter design the system remains in a state of sustained high-frequency dynamic instability under the action of repeated impulses. In turn, this sustained instability results in strong energy transfers from the directly excited oscillator to the lightweight nonlinear attachment; a feature that can be employed in energy harvesting applications. The theoretical predictions are confirmed by experimental results. National Science Foundation (U.S.) (Grant CMMI-1100722) 2015-07-31T12:25:58Z 2015-07-31T12:25:58Z 2013-11 2013-09 Article http://purl.org/eprint/type/JournalArticle 0739-3717 http://hdl.handle.net/1721.1/97929 Remick, Kevin, Alexander Vakakis, Lawrence Bergman, D. Michael McFarland, D. Dane Quinn, and Themistoklis P. Sapsis. “Sustained High-Frequency Dynamic Instability of a Nonlinear System of Coupled Oscillators Forced by Single or Repeated Impulses: Theoretical and Experimental Results.” Journal of Vibration and Acoustics 136, no. 1 (November 13, 2013): 011013. https://orcid.org/0000-0003-0302-0691 en_US http://dx.doi.org/10.1115/1.4025605 Journal of Vibration and Acoustics Creative Commons Attribution http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf ASME International Professor Sapsis via Angie Locknar |
| spellingShingle | Remick, Kevin Vakakis, Alexander McFarland, D. Michael Quinn, D. Dane Sapsis, Themistoklis Sustained High-Frequency Dynamic Instability of a Nonlinear System of Coupled Oscillators Forced by Single or Repeated Impulses: Theoretical and Experimental Results |
| title | Sustained High-Frequency Dynamic Instability of a Nonlinear System of Coupled Oscillators Forced by Single or Repeated Impulses: Theoretical and Experimental Results |
| title_full | Sustained High-Frequency Dynamic Instability of a Nonlinear System of Coupled Oscillators Forced by Single or Repeated Impulses: Theoretical and Experimental Results |
| title_fullStr | Sustained High-Frequency Dynamic Instability of a Nonlinear System of Coupled Oscillators Forced by Single or Repeated Impulses: Theoretical and Experimental Results |
| title_full_unstemmed | Sustained High-Frequency Dynamic Instability of a Nonlinear System of Coupled Oscillators Forced by Single or Repeated Impulses: Theoretical and Experimental Results |
| title_short | Sustained High-Frequency Dynamic Instability of a Nonlinear System of Coupled Oscillators Forced by Single or Repeated Impulses: Theoretical and Experimental Results |
| title_sort | sustained high frequency dynamic instability of a nonlinear system of coupled oscillators forced by single or repeated impulses theoretical and experimental results |
| url | http://hdl.handle.net/1721.1/97929 https://orcid.org/0000-0003-0302-0691 |
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