When a set of resonators is attached to a master structure, a bandgap opens in the vicinity of the resonance frequency. Then, using piezoelectric circuitry for instance, the spring constant coupling the resonators to the structure can be tuned thus allowing to actively control the resonance frequency and subsequently the position of the bandgap. In this study, we investigate the consequences of dynamically changing the resonance frequency of a resonant metamaterial on its dispersion diagram. In particular, the resonance frequency is modulated periodically in space and in time at a uniform speed in a wave-like fashion and at low frequencies of the same order of magnitude of the resonance frequency itself. A two-scale asymptotic homogenization approach shows that the modulated resonant metamaterial effectively behave as another resonant metamaterial with a different set of resonance frequencies. Changing the modulation speed reveals interesting effective dynamics whereby the bandgaps of the original metamaterial split, move, condense and merge to form new band structures. The results are illustrated and exemplified through the analytical study of a onedimensional elastic medium coupled with a continuous distribution of spring-mass oscillators resonating at low frequencies. The conclusions point towards possible applications in breaking time-reversal symmetry, active wave control and filtering.
Hussein Nassar, Andrew Norris, and Guoliang Huang, "Space-time modulations of phononic crystals (Conference Presentation)," Proc. SPIE 10170, Health Monitoring of Structural and Biological Systems 2017, 101700N (Presented at SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring: March 27, 2017; Published: 11 May 2017); https://doi.org/10.1117/12.2260125.5427850815001.
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