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.
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ASME 2011 International Mechanical Engineering Congress and Exposition
November 11–17, 2011
Denver, Colorado, USA
Conference Sponsors:
- ASME
ISBN:
978-0-7918-5497-6
PROCEEDINGS PAPER
Intensity-Dependent Dispersion in Nonlinear Phononic Layered Systems
Kevin L. Manktelow,
Kevin L. Manktelow
Georgia Institute of Technology, Atlanta, GA
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Michael J. Leamy,
Michael J. Leamy
Georgia Institute of Technology, Atlanta, GA
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Massimo Ruzzene
Massimo Ruzzene
Georgia Institute of Technology, Atlanta, GA
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Kevin L. Manktelow
Georgia Institute of Technology, Atlanta, GA
Michael J. Leamy
Georgia Institute of Technology, Atlanta, GA
Massimo Ruzzene
Georgia Institute of Technology, Atlanta, GA
Paper No:
IMECE2011-64933, pp. 557-565; 9 pages
Published Online:
August 1, 2012
Citation
Manktelow, KL, Leamy, MJ, & Ruzzene, M. "Intensity-Dependent Dispersion in Nonlinear Phononic Layered Systems." Proceedings of the 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. pp. 557-565. ASME. https://doi.org/10.1115/IMECE2011-64933
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