Band gaps appear in the frequency spectra of periodic materials and structures. In this work we examine flexural wave propagation in beams and investigate the effects of the various types and properties of periodicity on the frequency band structure, especially the location and width of band gaps. We consider periodicities involving the repeated spatial variation of material, geometry, boundary and/or suspended mass along the span of a beam. In our formulation, we implement Bloch’s theorem for elastic wave propagation and utilize Timoshenko beam theory for the kinematical description of the underlying flexural motion. For the calculation of the frequency band structure we use the transfer matrix method, derived here in generalized form to enable separate or combined consideration of the different types of periodicity. Our results provide band-gap maps as a function of the type and properties of periodicity, and as a prime focus we identify and mathematically characterize the condition for the transition between Bragg scattering and local resonance, each being a unique wave propagation mechanism, and show the effects of this transition on the lowest band gap. The analysis presented can be extended to multi-dimensional phononic crystals and acoustic metamaterials.
Skip Nav Destination
e-mail: [email protected]
Article navigation
January 2012
Research Papers
Wave Motion in Periodic Flexural Beams and Characterization of the Transition Between Bragg Scattering and Local Resonance Available to Purchase
Liao Liu,
Liao Liu
Department of Aerospace Engineering Sciences,
University of Colorado Boulder
, Boulder, CO 80309
Search for other works by this author on:
Mahmoud I. Hussein
Mahmoud I. Hussein
Department of Aerospace Engineering Sciences,
e-mail: [email protected]
University of Colorado Boulder
, Boulder, CO 80309
Search for other works by this author on:
Liao Liu
Department of Aerospace Engineering Sciences,
University of Colorado Boulder
, Boulder, CO 80309
Mahmoud I. Hussein
Department of Aerospace Engineering Sciences,
University of Colorado Boulder
, Boulder, CO 80309e-mail: [email protected]
J. Appl. Mech. Jan 2012, 79(1): 011003 (17 pages)
Published Online: November 14, 2011
Article history
Received:
July 7, 2010
Revised:
June 21, 2011
Posted:
July 13, 2011
Published:
November 14, 2011
Citation
Liu, L., and Hussein, M. I. (November 14, 2011). "Wave Motion in Periodic Flexural Beams and Characterization of the Transition Between Bragg Scattering and Local Resonance." ASME. J. Appl. Mech. January 2012; 79(1): 011003. https://doi.org/10.1115/1.4004592
Download citation file:
Get Email Alerts
Generalized incremental moduli of hyperelastic materials
J. Appl. Mech
Lennard-Jones Potential Parameters and Cut-Off Modifications for Layered Transition Metal Dichalcogenides
J. Appl. Mech (October 2025)
An Elastic Wedge Under Moment Loading: The Carothers Paradox Revisited
J. Appl. Mech (October 2025)
Nonlinear Normal Modes of Highly Flexible Cantilever Beams via Energy-Balance Based Approach
J. Appl. Mech (October 2025)
Related Articles
Multiple Scattering of Waves in Irregularly Laminated Composites
J. Appl. Mech (December,1980)
Quasi-One-Dimensional Periodic Structure with Locally Resonant Band Gap
J. Appl. Mech (January,2006)
Three-Dimensional Multiple Scattering of Elastic Waves by Spherical Inclusions
J. Vib. Acoust (December,2009)
Two-Dimensional In-Plane Elastic Waves in Curved-Tapered Square Lattice Frame Structure
J. Appl. Mech (March,2022)
Related Proceedings Papers
Related Chapters
Scattering of Out-Plane Line Source Load by a Shallow-Embedded Circular Lining Structure and the Ground Motion
Geological Engineering: Proceedings of the 1 st International Conference (ICGE 2007)
Study on Load Position Switching of Radial Scattering Dispenser
International Conference on Mechanical Engineering and Technology (ICMET-London 2011)
Model and Simulation of Low Elevation Ground-to-Air Fading Channel
International Conference on Instrumentation, Measurement, Circuits and Systems (ICIMCS 2011)