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A Physical Interpretation for Broken Reciprocity in Spatiotemporal Modulated Periodic Rods

[+] Author Affiliations
Jacopo Marconi, Gabriele Cazzulani, Francesco Braghin

Politecnico di Milano, Milano, Italy

Massimo Ruzzene

Georgia Institute of Technology, Atlanta, GA

Paper No. SMASIS2017-3877, pp. V002T03A027; 8 pages
doi:10.1115/SMASIS2017-3877
From:
  • ASME 2017 Conference on Smart Materials, Adaptive Structures and Intelligent Systems
  • Volume 2: Modeling, Simulation and Control of Adaptive Systems; Integrated System Design and Implementation; Structural Health Monitoring
  • Snowbird, Utah, USA, September 18–20, 2017
  • Conference Sponsors: Aerospace Division
  • ISBN: 978-0-7918-5826-4
  • Copyright © 2017 by ASME

abstract

Periodic systems have long been known for their peculiar characteristics in wave propagation and have been studied in many fields over the last century, going from electro-magnetics and optics to elastic structures, which drew an increasing interest in structural and mechanical engineering for vibration suppression and control spanning over broadband frequency ranges. Recently, on the stream of other studies conducted in different fields, spatiotemporal modulated elastic structures have been studied, showing promising results for wave control in that one-way propagation in the so called directional-bands can be achieved, constituting what may be called a mechanical diode. Despite of the fact that mathematical methods for the analysis of such structures have already been developed, often physics behind them is difficult to grasp. In this work, a simplified interpretation of the undergoing phenomena is thus given relating wave propagation in the mean to its physical characteristics as well as to modulation parameters. Exploiting Doppler effect and passive equivalent structures, it is shown that the broken reciprocity is due to the fact that opposite travelling waves effectively see two different periodic structures. To this aim the rod case is analysed for low modulation speeds and low modulation amplitudes; finally, in the light of the previous analysis, an explanation for First Brillouin Zone’s asymmetry is given.

Copyright © 2017 by ASME

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