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Wave Propagation in Membrane-Based Nonlinear Periodic Structures

[+] Author Affiliations
Raj K. Narisetti, Massimo Ruzzene, Michael J. Leamy

Georgia Institute of Technology, Atlanta, GA

Paper No. DETC2011-48700, pp. 213-220; 8 pages
doi:10.1115/DETC2011-48700
From:
  • ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 1: 23rd Biennial Conference on Mechanical Vibration and Noise, Parts A and B
  • Washington, DC, USA, August 28–31, 2011
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5478-5
  • Copyright © 2011 by ASME

abstract

Wave propagation in a periodic structure, formed by membrane elements on nonlinear elastic supports, is studied using a finite element discretization of a single unit cell followed by a perturbation analysis. The study is motivated in part by the need to study the dynamic behavior of micro-machined ultrasonic transducers (CMUTs). The requisite small parameter in the system arises from the ratio of the membrane to flexible support stiffness. The perturbation approach recovers linear Bloch formalism at first order, and amplitude-dependent dispersion corrections at higher orders. The procedure is used to generate weakly nonlinear band diagrams, which can in turn be used to identify amplitude-dependent bandgaps and group velocities. These diagrams also reveal that the strongest amplitude dependency occurs in high-frequency optical modes. Ultimately, the predicted dispersion behavior will be useful in assessing inter-element coupling and identifying effective excitation strategies for actuating CMUTs.

Copyright © 2011 by ASME

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