### Abstract

We examine analytically and experimentally a new phenomenon of 'continuous resonance scattering' in an impulsively excited, two-mass oscillating system. This system consists of a grounded damped linear oscillator with a light, strongly nonlinear attachment. Previous numerical simulations revealed that for certain levels of initial excitation, the system engages in a special type of response that appears to track a solution branch formed by the so-called 'impulsive orbits' of this system. By this term we denote the periodic (under conditions of resonance) or quasi-periodic (under conditions of non-resonance) responses of the system when a single impulse is applied to the linear oscillator with the system being initially at rest. By varying the magnitude of the impulse we obtain a manifold of impulsive orbits in the frequency-energy plane. It appears that the considered damped system is capable of entering into a state of continuous resonance scattering, whereby it tracks the impulsive orbit manifold with decreasing energy. Through analytical treatment of the equations of motion, a direct relationship is established between the frequency of the nonlinear attachment and the amplitude of the linear oscillator response, and a prediction of the system response during continuous scattering resonance is provided. Experimental results confirm the analytical predictions.

Original language | English (US) |
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Title of host publication | ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011 |

Pages | 839-845 |

Number of pages | 7 |

Edition | PARTS A AND B |

DOIs | |

State | Published - Dec 1 2011 |

Event | ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011 - Washington, DC, United States Duration: Aug 28 2011 → Aug 31 2011 |

### Publication series

Name | Proceedings of the ASME Design Engineering Technical Conference |
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Number | PARTS A AND B |

Volume | 4 |

### Other

Other | ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011 |
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Country | United States |

City | Washington, DC |

Period | 8/28/11 → 8/31/11 |

### Fingerprint

### ASJC Scopus subject areas

- Modeling and Simulation
- Mechanical Engineering
- Computer Science Applications
- Computer Graphics and Computer-Aided Design

### Cite this

*ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011*(PARTS A AND B ed., pp. 839-845). (Proceedings of the ASME Design Engineering Technical Conference; Vol. 4, No. PARTS A AND B). https://doi.org/10.1115/DETC2011-47950

**Damped transition of a strongly nonlinear system of coupled oscillators into a state of continuous resonance scattering.** / Andersen, David; Wang, Xingyuan; Starosvetsky, Yuli; Remick, Kevin; Vakakis, Alexander F; Mane, Mercedes; Hubbard, Sean; Bergman, Lawrence.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011.*PARTS A AND B edn, Proceedings of the ASME Design Engineering Technical Conference, no. PARTS A AND B, vol. 4, pp. 839-845, ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011, Washington, DC, United States, 8/28/11. https://doi.org/10.1115/DETC2011-47950

}

TY - GEN

T1 - Damped transition of a strongly nonlinear system of coupled oscillators into a state of continuous resonance scattering

AU - Andersen, David

AU - Wang, Xingyuan

AU - Starosvetsky, Yuli

AU - Remick, Kevin

AU - Vakakis, Alexander F

AU - Mane, Mercedes

AU - Hubbard, Sean

AU - Bergman, Lawrence

PY - 2011/12/1

Y1 - 2011/12/1

N2 - We examine analytically and experimentally a new phenomenon of 'continuous resonance scattering' in an impulsively excited, two-mass oscillating system. This system consists of a grounded damped linear oscillator with a light, strongly nonlinear attachment. Previous numerical simulations revealed that for certain levels of initial excitation, the system engages in a special type of response that appears to track a solution branch formed by the so-called 'impulsive orbits' of this system. By this term we denote the periodic (under conditions of resonance) or quasi-periodic (under conditions of non-resonance) responses of the system when a single impulse is applied to the linear oscillator with the system being initially at rest. By varying the magnitude of the impulse we obtain a manifold of impulsive orbits in the frequency-energy plane. It appears that the considered damped system is capable of entering into a state of continuous resonance scattering, whereby it tracks the impulsive orbit manifold with decreasing energy. Through analytical treatment of the equations of motion, a direct relationship is established between the frequency of the nonlinear attachment and the amplitude of the linear oscillator response, and a prediction of the system response during continuous scattering resonance is provided. Experimental results confirm the analytical predictions.

AB - We examine analytically and experimentally a new phenomenon of 'continuous resonance scattering' in an impulsively excited, two-mass oscillating system. This system consists of a grounded damped linear oscillator with a light, strongly nonlinear attachment. Previous numerical simulations revealed that for certain levels of initial excitation, the system engages in a special type of response that appears to track a solution branch formed by the so-called 'impulsive orbits' of this system. By this term we denote the periodic (under conditions of resonance) or quasi-periodic (under conditions of non-resonance) responses of the system when a single impulse is applied to the linear oscillator with the system being initially at rest. By varying the magnitude of the impulse we obtain a manifold of impulsive orbits in the frequency-energy plane. It appears that the considered damped system is capable of entering into a state of continuous resonance scattering, whereby it tracks the impulsive orbit manifold with decreasing energy. Through analytical treatment of the equations of motion, a direct relationship is established between the frequency of the nonlinear attachment and the amplitude of the linear oscillator response, and a prediction of the system response during continuous scattering resonance is provided. Experimental results confirm the analytical predictions.

UR - http://www.scopus.com/inward/record.url?scp=84863589962&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84863589962&partnerID=8YFLogxK

U2 - 10.1115/DETC2011-47950

DO - 10.1115/DETC2011-47950

M3 - Conference contribution

AN - SCOPUS:84863589962

SN - 9780791854815

T3 - Proceedings of the ASME Design Engineering Technical Conference

SP - 839

EP - 845

BT - ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011

ER -