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Intensity-Dependent Dispersion in Nonlinear Phononic Layered Systems

[+] Author Affiliations
Kevin L. Manktelow, Michael J. Leamy, Massimo Ruzzene

Georgia Institute of Technology, Atlanta, GA

Paper No. IMECE2011-64933, pp. 557-565; 9 pages
  • ASME 2011 International Mechanical Engineering Congress and Exposition
  • Volume 11: Nano and Micro Materials, Devices and Systems; Microsystems Integration
  • Denver, Colorado, USA, November 11–17, 2011
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-5497-6
  • Copyright © 2011 by ASME


Phononic crystals are typically considered to operate in regimes where a linear constitutive relationship provides an adequate representation. For high intensity wave propagation, however, weak nonlinearities can affect performance. For example, a cubic nonlinearity gives rise to frequency shifting and thus a shift in band gap location. In the study of nonlinear optics, a cubic term has been treated using a quasi-linear constitutive relationship with intensity dependent properties. This technique is explored herein for generating nonlinear dispersion relationships for the elastic case. In addition, a perturbation method developed previously for discrete systems, used in conjunction with a finite element discretization, is proposed as an alternative dispersion analysis tool. Simulations of the fully nonlinear governing equations are provided as validation of the predicted dispersion curves.

Copyright © 2011 by ASME



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