Abstract
We are concerned with controlling wave propagation in an elastic medium by engineering its dispersive properties. To this end, we discuss a flexible and systematic framework for designing the material composition of the unit cell of a periodic medium when given a target dispersion relation or, equivalently, a target group velocity profile at a user-defined frequency range. We cast the inverse medium design problem as a dispersion-constrained optimization problem that minimizes the distance between the target and the computed group velocity profiles. We rely on the Hellmann–Feynman theorem to obtain the computed group velocity of a trial unit cell, and use a gradient-based algorithm to drive the engineered medium’s material properties to convergence. We numerically demonstrate the capabilities of the approach using scalar waves in one and two dimensions. We also use the method to design metamaterials exhibiting user-defined omnidirectional band gaps and to provide numerical evidence of the metamaterial’s intended performance via time-domain simulations.
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Acknowledgments
We wish to thank Professor Andrea Alù for fruitful discussions, as well as the anonymous reviewers for their constructive comments.
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Published In
Journal of Engineering Mechanics
Volume 145 • Issue 12 • December 2019
Copyright
©2019 American Society of Civil Engineers.
History
Received: Nov 25, 2018
Accepted: Apr 24, 2019
Published online: Sep 19, 2019
Published in print: Dec 1, 2019
Discussion open until: Feb 19, 2020
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