### Abstract

We explore the conservative and dissipative dynamics of a two-degree-of-freedom (2-DoF) system consisting of a linear oscillator and a lightweight nonlinear rotator inertially coupled to it. When the total energy of the system is large enough, the motion of the rotator is, generically, chaotic. Moreover, we show that if the damping of the rotator is sufficiently small and the damping of the linear oscillator is even smaller, then the system passes through a cascade of resonance captures (transient internal resonances) as the total energy gradually decreases. Rather unexpectedly, all these captures have the same principal frequency but correspond to different nonlinear normal modes (NNMs). In each NNM, the rotator is phaselocked into periodic motion with two frequencies. The NNMs differ by the ratio of these frequencies, which is approximately an integer for each NNM. Essentially non-integer ratios lead to incommensurate periods of 'slow' and 'fast' motions of the rotator and, thus, to its chaotic behavior between successive resonance captures. Furthermore, we show that these cascades of resonance captures lead to targeted energy transfer (TET) from the linear oscillator to the rotator, with the latter serving, in essence, as a nonlinear energy sink (NES). Since the inertially-coupled NES that we consider has no linearized natural frequency, it is capable of engaging in resonance with the linear oscillator over broad frequency and energy ranges. The results presented herein indicate that the proposed rotational NES appears to be a promising design for broadband shock mitigation and vibration energy harvesting.

Original language | English (US) |
---|---|

Pages (from-to) | 1693-1704 |

Number of pages | 12 |

Journal | Nonlinear Dynamics |

Volume | 69 |

Issue number | 4 |

DOIs | |

State | Published - Sep 1 2012 |

### Fingerprint

### Keywords

- Nonlinear targeted energy transfer
- Resonance capture
- Rotator

### ASJC Scopus subject areas

- Control and Systems Engineering
- Aerospace Engineering
- Ocean Engineering
- Mechanical Engineering
- Applied Mathematics
- Electrical and Electronic Engineering

### Cite this

*Nonlinear Dynamics*,

*69*(4), 1693-1704. https://doi.org/10.1007/s11071-012-0379-1

**Resonance captures and targeted energy transfers in an inertially-coupled rotational nonlinear energy sink.** / Sigalov, G.; Gendelman, O. V.; AL-Shudeifat, M. A.; Manevitch, L. I.; Vakakis, A. F.; Bergman, L. A.

Research output: Contribution to journal › Article

*Nonlinear Dynamics*, vol. 69, no. 4, pp. 1693-1704. https://doi.org/10.1007/s11071-012-0379-1

}

TY - JOUR

T1 - Resonance captures and targeted energy transfers in an inertially-coupled rotational nonlinear energy sink

AU - Sigalov, G.

AU - Gendelman, O. V.

AU - AL-Shudeifat, M. A.

AU - Manevitch, L. I.

AU - Vakakis, A. F.

AU - Bergman, L. A.

PY - 2012/9/1

Y1 - 2012/9/1

N2 - We explore the conservative and dissipative dynamics of a two-degree-of-freedom (2-DoF) system consisting of a linear oscillator and a lightweight nonlinear rotator inertially coupled to it. When the total energy of the system is large enough, the motion of the rotator is, generically, chaotic. Moreover, we show that if the damping of the rotator is sufficiently small and the damping of the linear oscillator is even smaller, then the system passes through a cascade of resonance captures (transient internal resonances) as the total energy gradually decreases. Rather unexpectedly, all these captures have the same principal frequency but correspond to different nonlinear normal modes (NNMs). In each NNM, the rotator is phaselocked into periodic motion with two frequencies. The NNMs differ by the ratio of these frequencies, which is approximately an integer for each NNM. Essentially non-integer ratios lead to incommensurate periods of 'slow' and 'fast' motions of the rotator and, thus, to its chaotic behavior between successive resonance captures. Furthermore, we show that these cascades of resonance captures lead to targeted energy transfer (TET) from the linear oscillator to the rotator, with the latter serving, in essence, as a nonlinear energy sink (NES). Since the inertially-coupled NES that we consider has no linearized natural frequency, it is capable of engaging in resonance with the linear oscillator over broad frequency and energy ranges. The results presented herein indicate that the proposed rotational NES appears to be a promising design for broadband shock mitigation and vibration energy harvesting.

AB - We explore the conservative and dissipative dynamics of a two-degree-of-freedom (2-DoF) system consisting of a linear oscillator and a lightweight nonlinear rotator inertially coupled to it. When the total energy of the system is large enough, the motion of the rotator is, generically, chaotic. Moreover, we show that if the damping of the rotator is sufficiently small and the damping of the linear oscillator is even smaller, then the system passes through a cascade of resonance captures (transient internal resonances) as the total energy gradually decreases. Rather unexpectedly, all these captures have the same principal frequency but correspond to different nonlinear normal modes (NNMs). In each NNM, the rotator is phaselocked into periodic motion with two frequencies. The NNMs differ by the ratio of these frequencies, which is approximately an integer for each NNM. Essentially non-integer ratios lead to incommensurate periods of 'slow' and 'fast' motions of the rotator and, thus, to its chaotic behavior between successive resonance captures. Furthermore, we show that these cascades of resonance captures lead to targeted energy transfer (TET) from the linear oscillator to the rotator, with the latter serving, in essence, as a nonlinear energy sink (NES). Since the inertially-coupled NES that we consider has no linearized natural frequency, it is capable of engaging in resonance with the linear oscillator over broad frequency and energy ranges. The results presented herein indicate that the proposed rotational NES appears to be a promising design for broadband shock mitigation and vibration energy harvesting.

KW - Nonlinear targeted energy transfer

KW - Resonance capture

KW - Rotator

UR - http://www.scopus.com/inward/record.url?scp=84866065692&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84866065692&partnerID=8YFLogxK

U2 - 10.1007/s11071-012-0379-1

DO - 10.1007/s11071-012-0379-1

M3 - Article

AN - SCOPUS:84866065692

VL - 69

SP - 1693

EP - 1704

JO - Nonlinear Dynamics

JF - Nonlinear Dynamics

SN - 0924-090X

IS - 4

ER -