Session: VIB-03-03: Dynamics & Waves in Solids and Metamaterials III

Paper Number: 97569

97569 - Band Gap Resonances in Finite Periodic Bilayer Beams 

Infinite periodic structures exhibit band gaps that attenuate waves propagating in the medium through Bragg scattering. However, their finite counterparts in practical applications involve periodicity termination at the boundaries of the system, which may result in resonant frequencies inside the band gap (i.e., band gap resonances.) Prior studies have shown the existence conditions for band gap resonances in finite periodic spring-mass models or semi-infinite phononic crystals under limited boundary conditions. In this study, we numerically investigate the existence of band gap resonances and corresponding mode shapes in finite bilayer beams with more general boundary conditions. We adopt mathematical models for longitudinal and transverse vibrations of beams to compute dispersion relations and eigenfrequencies of the finite beams. Then, we present the existence of band gap resonance within the first band gap of a bilayer beam depending on various boundary conditions, symmetricity of the finite structure, and ratios of stiffness, density, and cross-section area. We confirm that the results with fixed-fixed or free-free boundary conditions are consistent with the previous studies and present other sets of boundary conditions that allow band gap resonances in longitudinal or transverse vibrations of bilayer beams. We also show that the mode shapes associated with the band gap resonances exhibit exponentially decaying amplitude profiles starting from the boundaries. Finally, we show the frequency response at the truncated boundaries due to boundary loading.

Presenting Author: Sangwon Park University of Illinois at Urbana-Champaign

Presenting Author Biography: Sangwon Park is a Ph.D. student in Mechanical Engineering at the University of Illinois at Urbana-Champaign. He completed his B.S. and M.S. in Mechanical Engineering at Yonsei University, Seoul, Korea with a focus on structural vibration and vibro-acoustics. His current research interests include phononic crystals for passive flow control and wave propagation in finite phononic crystals.

Authors:

Sangwon Park University of Illinois at Urbana-Champaign
Kathryn Matlack University of Illinois at Urbana-Champaign