Optimization under Uncertainty of Nonlinear Energy Sinks
Nonlinear Energy Sinks (NESs) are a promising technique for passively reducing the amplitude of vibrations, especially for use as energy pumping devices for buildings under seismic loading. NESs were introduced and detailed in Vakakis (2008). Through nonlinear stiffness properties, a NES is able to passively and irreversibly absorb energy. Two examples of a NES are given in the following figures.

Figure 1: Reversible exchange of energy between main system (red) and NES (black).

Figure 2: Irreversible exchange of energy between main system (red) and NES (black).

Unlike the traditional Tuned Mass Damper (TMD), the NES has no inherent natural frequency and is able to absorb energy over a wide range of frequencies. The efficiency of the NES, however, is extremely sensitive to small perturbations in design parameters or initial conditions. The sensitivity of the NES is shown in the figure below:



Figure 3: Example of discontinuity in efficiency metric for variations in NES design parameters.

In many cases, it has been observed that the most efficient NES designs are very close to low efficiency regions in the design space. In order to optimize NES devices, the high sensitivity of NES to uncertainty, with almost discontinuous behaviors, requires specific reliability-based design optimization (RBDO) techniques.

This research uses tailored classification and meta-modeling techniques to accurately model the behavior of the NES. These techniques are based on tools such as support vector machines (SVM) and Kriging, as well as a fundamental understanding of NES behavior. For further details see Boroson and Missoum (2014) and Boroson and Missoum (2015).

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Vakakis, A. S., Gendelman, O. V., Bergman, L. A., McFarland, D.K., Kerschen, G., and Lee, Y. S., Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems, Springer Science and Buisiness Media, vol 156: 2008.

Boroson, E., and Missoum, S.Reliability-based Design Optimization of Nonlinear Energy SinksProceedings of the 11th World Congress of Structural and Multidisciplinary Optimisation (WCSMO-11), Sydney, Australia: 2015.

Boroson, E.Missoum, S.Mattei, P. - O., and Vergez, C., Optimization Under Uncertainty of Nonlinear energy Sinks, Proceedings of the ASME International Design and Engineering Technical Conferences and Computers and Information in Engineering Conference, Buffalo, NY: American Society of Mechanical Engineers, 2014.

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