, Volume 53, Issue 11–12, pp 3105–3122 | Cite as

Band gap synthesis in elastic monatomic lattices via input shaping

  • H. Al Ba’ba’a
  • J. Callanan
  • M. Nouh
  • T. Singh


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.


Wave propagation Lattices Band gap Input shaping 


Compliance with ethical standards

Conflicts of interest

The authors declare that they have no conflict of interest.


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of Mechanical and Aerospace EngineeringUniversity at Buffalo (SUNY)BuffaloUSA

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