Band gap synthesis in elastic monatomic lattices via input shaping
This work describes control-theoretic methods for inducing a band gap-like behavior in elastic monatomic lattices. The dynamics of the system under consideration are derived in detail. Open-loop pre-filtering techniques, in the form of Posicast and user-selected time delay filters, are then utilized to eliminate specific frequency contents from the response of the multi-degree of freedom spring-mass chain. The input shaping approach is used to synthesize one or more band gaps in a homogenous lattice that can be designed to resemble Bragg-scattering in phononic crystals, as well as local resonance effects in acoustic metamaterials. The presence of the synthesized band gaps in the lattice’s dispersion behavior is validated using a spatiotemporal Fourier transform of the system’s impulse response as well as the frequency response of the end-to-end transfer function. Finally, an analysis of the control effort required to cancel the targeted system poles is carried out.
KeywordsWave propagation Lattices Band gap Input shaping
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Conflicts of interest
The authors declare that they have no conflict of interest.
- 1.Pai F, Huang G (2015) Theory and design of acoustic metamaterials. (the International Society for Optics and Photonics (SPIE))Google Scholar
- 2.Deymier PA (2013) Acoustic metamaterials and phononic crystals, vol 173. Springer Science, BerlinGoogle Scholar
- 22.Sugino C, Xia Y, Leadenham S, Ruzzene M, Erturk A (2016) A general theory for bandgap estimation in locally resonant metastructures. arXiv preprint arXiv:1612.03130
- 27.Kased R, Singh T (2010) Rest-to-rest motion of an experimental flexible structure subject to friction: linear programming approach. J Vib Acoust 132(1)Google Scholar
- 29.Pereira E, Trapero JR, Díaz IM, Feliu V (2009) Adaptive input shaping for manoeuvring flexible structures using an algebraic identification technique. Automatica 45(4): 1046Google Scholar
- 38.Miu D (1993) Mechatronics- electromechanics and contromechanics. Springer, BerlinGoogle Scholar
- 39.Wie B, Bryson Jr AE (1981) Modeling and control of flexible space structuresGoogle Scholar
- 42.Tuttle TD, Seering WP (1994) in American Control Conference. A zero-placement technique for designing shaped inputs to suppress multiple-mode vibration, vol. 3 (IEEE), vol. 3, pp. 2533–2537Google Scholar
- 44.Gürleyük S, Cinal Ş (2007) Robust three-impulse sequence input shaper design. J Vib Control 13(12):1807Google Scholar
- 47.Elliott JF (1953) The characteristic roots of certain real symmetric matrices, The characteristic roots of certain real symmetric matrices. Master’s thesis, University of Tennessee, KnoxvilleGoogle Scholar