Abstract
We consider the response of a linear structural system when coupled to an attachment containing strong or even essential nonlinearities. For this system, the attachment, designated as a nonlinear energy sink, is designed as a nonlinear vibration absorber, serving to dissipate energy from the structural system. Moreover, the attachment not only leads to a reduction in the total energy of the system, but also nonlinearly couples together the vibration modes of the linear structural system. When the structure is impulsively loaded, the nonlinear energy sink serves to both dissipate and redistribute energy, thus enhancing the observed structural dissipation. The effect of the nonlinear attachment on the linear primary system can be quantified in terms of equivalent measures for the damping and frequency of each mode, derived through consideration of the instantaneous energy balance in each mode. The influence of the nonlinear energy sink on the structural response is illustrated with an impulsively forced two-degree-of-freedom primary system, representing a two-story structure, with different types of nonlinear energy sink attached to the top floor. We perform optimization studies in order to design the nonlinear energy sink for optimal shock mitigation of the primary system. The proposed methodology is based only on measured time series without resorting to frequency analysis. As such, it is valid for strongly nonlinear systems as well as for systems with nonsmooth nonlinearities, and is suited to both simulated and experimental results. Finally, an experimental validation of the enhanced dissipation introduced by the nonlinear energy sink is provided, and the experimental response is compared against numerical simulation of the corresponding analytical model to illustrate the effectiveness of the nonlinear energy sink design. Thus, we analytically predict and experimentally verify the efficacy of the nonlinear energy sink to significantly reduce the response of the two degree-of-freedom system subject to shock excitation.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 122-146 |
| Number of pages | 25 |
| Journal | Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics |
| Volume | 226 |
| Issue number | 2 |
| DOIs | |
| State | Published - Jun 1 2012 |
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Keywords
- Structural damping
- essential nonlinearities
- experimental analysis
- modeling and simulation
- shock mitigation
ASJC Scopus subject areas
- Condensed Matter Physics
- Mechanical Engineering
Cite this
Equivalent modal damping, stiffening and energy exchanges in multi-degree-of-freedom systems with strongly nonlinear attachments. / Quinn, D. Dane; Hubbard, Sean; Wierschem, Nicholas; Al-Shudeifat, Mohammad A.; Ott, Richard J.; Luo, Jie; Spencer, Billie F.; McFarland, D. Michael; Vakakis, Alexander F.; Bergman, Lawrence A.
In: Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics, Vol. 226, No. 2, 01.06.2012, p. 122-146.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Equivalent modal damping, stiffening and energy exchanges in multi-degree-of-freedom systems with strongly nonlinear attachments
AU - Quinn, D. Dane
AU - Hubbard, Sean
AU - Wierschem, Nicholas
AU - Al-Shudeifat, Mohammad A.
AU - Ott, Richard J.
AU - Luo, Jie
AU - Spencer, Billie F.
AU - McFarland, D. Michael
AU - Vakakis, Alexander F.
AU - Bergman, Lawrence A.
PY - 2012/6/1
Y1 - 2012/6/1
N2 - We consider the response of a linear structural system when coupled to an attachment containing strong or even essential nonlinearities. For this system, the attachment, designated as a nonlinear energy sink, is designed as a nonlinear vibration absorber, serving to dissipate energy from the structural system. Moreover, the attachment not only leads to a reduction in the total energy of the system, but also nonlinearly couples together the vibration modes of the linear structural system. When the structure is impulsively loaded, the nonlinear energy sink serves to both dissipate and redistribute energy, thus enhancing the observed structural dissipation. The effect of the nonlinear attachment on the linear primary system can be quantified in terms of equivalent measures for the damping and frequency of each mode, derived through consideration of the instantaneous energy balance in each mode. The influence of the nonlinear energy sink on the structural response is illustrated with an impulsively forced two-degree-of-freedom primary system, representing a two-story structure, with different types of nonlinear energy sink attached to the top floor. We perform optimization studies in order to design the nonlinear energy sink for optimal shock mitigation of the primary system. The proposed methodology is based only on measured time series without resorting to frequency analysis. As such, it is valid for strongly nonlinear systems as well as for systems with nonsmooth nonlinearities, and is suited to both simulated and experimental results. Finally, an experimental validation of the enhanced dissipation introduced by the nonlinear energy sink is provided, and the experimental response is compared against numerical simulation of the corresponding analytical model to illustrate the effectiveness of the nonlinear energy sink design. Thus, we analytically predict and experimentally verify the efficacy of the nonlinear energy sink to significantly reduce the response of the two degree-of-freedom system subject to shock excitation.
AB - We consider the response of a linear structural system when coupled to an attachment containing strong or even essential nonlinearities. For this system, the attachment, designated as a nonlinear energy sink, is designed as a nonlinear vibration absorber, serving to dissipate energy from the structural system. Moreover, the attachment not only leads to a reduction in the total energy of the system, but also nonlinearly couples together the vibration modes of the linear structural system. When the structure is impulsively loaded, the nonlinear energy sink serves to both dissipate and redistribute energy, thus enhancing the observed structural dissipation. The effect of the nonlinear attachment on the linear primary system can be quantified in terms of equivalent measures for the damping and frequency of each mode, derived through consideration of the instantaneous energy balance in each mode. The influence of the nonlinear energy sink on the structural response is illustrated with an impulsively forced two-degree-of-freedom primary system, representing a two-story structure, with different types of nonlinear energy sink attached to the top floor. We perform optimization studies in order to design the nonlinear energy sink for optimal shock mitigation of the primary system. The proposed methodology is based only on measured time series without resorting to frequency analysis. As such, it is valid for strongly nonlinear systems as well as for systems with nonsmooth nonlinearities, and is suited to both simulated and experimental results. Finally, an experimental validation of the enhanced dissipation introduced by the nonlinear energy sink is provided, and the experimental response is compared against numerical simulation of the corresponding analytical model to illustrate the effectiveness of the nonlinear energy sink design. Thus, we analytically predict and experimentally verify the efficacy of the nonlinear energy sink to significantly reduce the response of the two degree-of-freedom system subject to shock excitation.
KW - Structural damping
KW - essential nonlinearities
KW - experimental analysis
KW - modeling and simulation
KW - shock mitigation
UR - http://www.scopus.com/inward/record.url?scp=84865691659&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84865691659&partnerID=8YFLogxK
U2 - 10.1177/1464419311432671
DO - 10.1177/1464419311432671
M3 - Article
AN - SCOPUS:84865691659
VL - 226
SP - 122
EP - 146
JO - Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics
JF - Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics
SN - 1464-4193
IS - 2
ER -