The paper investigates wave dispersion in two-dimensional, weakly nonlinear periodic lattices. A perturbation approach, originally developed for one-dimensional systems and extended herein, allows for closed-form determination of the effects nonlinearities have on dispersion and group velocity. These expressions are used to identify amplitude-dependent bandgaps, and wave directivity in the anisotropic setting. The predictions from the perturbation technique are verified by numerically integrating the lattice equations of motion. For small amplitude waves, excellent agreement is documented for dispersion relationships and directivity patterns. Further, numerical simulations demonstrate that the response in anisotropic nonlinear lattices is characterized by amplitude-dependent “dead zones.”
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December 2011
Research Papers
A Perturbation Approach for Analyzing Dispersion and Group Velocities in Two-Dimensional Nonlinear Periodic Lattices
R. K. Narisetti,
R. K. Narisetti
School of Aerospace Engineering,
e-mail: rajknarisetti@gatech.edu
GA Institute of Technology
, Atlanta, GA 30332
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M. Ruzzene,
M. Ruzzene
School of Aerospace Engineering, GA Institute of Technology, Atlanta, GA 30332; School of Mechanical Engineering,
GA Institute of Technology
, Atlanta, GA 30332
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M. J. Leamy
M. J. Leamy
School of Mechanical Engineering,
GA Institute of Technology
, Atlanta, GA 30332
Search for other works by this author on:
R. K. Narisetti
School of Aerospace Engineering,
GA Institute of Technology
, Atlanta, GA 30332e-mail: rajknarisetti@gatech.edu
M. Ruzzene
School of Aerospace Engineering, GA Institute of Technology, Atlanta, GA 30332; School of Mechanical Engineering,
GA Institute of Technology
, Atlanta, GA 30332
M. J. Leamy
School of Mechanical Engineering,
GA Institute of Technology
, Atlanta, GA 30332J. Vib. Acoust. Dec 2011, 133(6): 061020 (12 pages)
Published Online: December 1, 2011
Article history
Received:
November 24, 2009
Revised:
March 22, 2011
Online:
December 1, 2011
Published:
December 1, 2011
Citation
Narisetti, R. K., Ruzzene, M., and Leamy, M. J. (December 1, 2011). "A Perturbation Approach for Analyzing Dispersion and Group Velocities in Two-Dimensional Nonlinear Periodic Lattices." ASME. J. Vib. Acoust. December 2011; 133(6): 061020. https://doi.org/10.1115/1.4004661
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