160 M.J. Mazzoleni et al. Fig. 13.5 These plots show the experimental results of various frequency sweeps in the pendulum assembly, and it can be seen that two distinct propagation zones exist in each well, with a bandgap region in between. Plot (a) shows the forward frequency sweep for the deep well, plot (b) shows the reverse frequency sweep for the deep well, plot (c) shows the forward frequency sweep for the shallow well, and plot (d) shows the reverse frequency sweep for the shallow well. The first oscillator behaves differently from the rest because it is being directly driven by the vertical shaker. The last oscillator also behaves slightly differently due to boundary effects 13.4 Conclusion This paper presents a mathematical model that describes the bandgap structure for a 1D chain of bistable oscillators, and shows that introducing an asymmetric bistability into the system will result in two distinct bandgap structures. Bandgaps are attenuation zones that exist between two propagation zones, and it is often desirable to tune these bandgaps for specific applications. This paper shows that the system can be tuned so that it can achieve amplitude dependent filtering through passive bandgap reconfiguration. This enables waves to propagate through the system as long their amplitude is below a critical threshold. After crossing the threshold, passive bandgap reconfiguration occurs and waves are attenuated instead of propagated through the system. An experimental system was constructed to demonstrate this phenomenon, and comparisons between experiments and theory show good agreement. Acknowledgements The authors would like to thank Xiao Wen, Jake Greenstein, Charlie Arentzen, and Jared Little for their contributions to this project. This project was primarily funded by the NSF through grants CMMI-1300307 and CMMI-1300658, and it was also supported by the ARO.
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