162 M.J. Mazzoleni et al. −200 −100 0 100 200 ˙θ (deg/s) a b 0 1 2 3 4 5 −0.1 0 0.1 Time(min) ˙z (m/s) 0 1 2 3 4 5 1 5 10 14 −20 −10 0 10 20 Time(min) Oscillator# θ (deg) c Fig. 13.7 These plots demonstrates amplitude dependent filtering through passive bandgap reconfiguration. Plot (a) analyzes the fifth oscillator in the pendulum assembly during an amplitude sweep, and shows how the amplitude of oscillations increases until a bifurcation occurs and the system transitions from the propagation zone in the shallow well to the attenuation zone in the deep well. After transient effects fade away, the system’s oscillations are almost zero, even though the amplitude of excitation for the system is still increasing. Plot (b) verifies that the excitation amplitude was steadily increasing throughout the experiment (Pz is the velocity of the vertical shaker input). Plot (c) shows that all of the pendulums transitioned from the shallow well to the deep well nearly simultaneously. The first oscillator behaves differently from the rest because it is being directly driven by the vertical shaker References 1. Friesecke G, Wattis JAD (1994) Existence theorem for solitary waves on lattices. Commun Math Phys 161:391–418 2. Lazaridi AN, Nesterenko VF (1985) Observation of a new type of solitary waves in a one-dimensional granular medium. J Appl Mech Tech Phys 26:405–408 3. Mead DJ (1996) Wave propagation in continuous periodic structures: research contributions from Southampton, 1964–1995. J Sound Vib 190:495–524 4. Brillouin L (1953) Wave propagation in periodic structures. Dover, New York 5. Kushwaha MS, Halevi P, Dobrzynski L, Djafari-Rouhani B (1993) Acoustic band structure of periodic elastic composites. Phys Rev Lett 71:2022–2025 6. Kushwaha MS, Halevi P, Martinez G, Dobrzynski L, Djafari-Rouhani B (1994) Theory of acoustic band-structure of periodic elastic composites. Phys Rev B Condens Matter Mater Phys 49:2313–2322 7. Daraio C, Nesterenko VF, Herbold EB, Jinn S (2006) Energy trapping and shock disintegration in a composite granular medium. Phys Rev Lett 96:058002 8. Zhou XZ, Wang YS, Zhang C (2009) Effects of material parameters on elastic band gaps of two-dimensional solid phononic crystals. J Appl Phys 106:014903 9. Sun HX, Zhang SY, Shui XJ (2012) A tunable acoustic diode made by a metal plate with periodical structure. J Appl Phys 100:103507 10. Doney R, Sen S (2006) Decorated, tapered, and highly nonlinear granular chain. Phys Rev Lett 97:155502 11. Zhou W, Mackie DM, Taysing-Lara M, Dang G, Newman PG, Svensson S (2006) Novel reconfigurable semiconductor photonic crystal-mems device. Solid State Electron 50:908–913 12. Edalati A, Boutayeb H, Denidni TA (2007) Band structure analysis of reconfigurable metallic crystals: effect of active elements. J Electromagn Waves Appl 21:2421–2430 13. Herbold EB, Kim J, Nesterenko VF, Wang SY, Daraio C (2009) Pulse propagation in a linear and nonlinear diatomic periodic chain: effects of acoustic frequency band-gap. Acta Mech 205:85–103 14. Yang XS, Wang BZ, Zhang Y (2004) Pattern-reconfigurable quasi-yagi microstrip antenna using a photonic band gap structure. Microw Opt Technol Lett 42:296–297 15. Bernard BP, Mann BP (2013) Passive band-gap reconfiguration born from bifurcation asymmetry. Phys Rev E Stat Nonlinear Soft Matter Phys 88:052903 16. Bernard BP, Mazzoleni MJ, Garraud N, Arnold DP, Mann BP (2014) Experimental investigation of bifurcation induced bandgap reconfiguration. J Appl Phys 116:084904 17. Jensen JS (2003) Phononic band gaps and vibrations in one- and two-dimensional mass-spring structures. J Sound Vib 266:1053–1078
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