Date of Award

Spring 11-17-2018

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

First Advisor

Mahmoud I. Hussein

Second Advisor

Sedat Biringen

Third Advisor

Carlos Felippa

Fourth Advisor

Francisco López Jiménez

Fifth Advisor

Fatemeh Pourahmadian

Abstract

Phononic materials comprise microstructures engineered for unique, and often exotic, acoustic or elastic wave-propagation characteristics. For example, an elastic metamaterial, which is a type of phononic material, may be tuned to exhibit a band gap at frequencies corresponding to wavelengths much longer than the size of the microstructure. A common approach for realizing such extreme dynamical properties is to intrinsically distribute local resonators along the domain of the material. This concept has been extensively studied in the context of low-frequency vibration shielding, subwavelength focusing and imaging, and acoustic/elastic cloaking. However, despite the importance of dissipation in wave propagation, the effects of damping are often neglected in these applications, and in the elastodynamics literature in general. Incorporating damping in the treatment of metamaterials does not only provide a more realistic description of their dynamical behavior, but also allows one to understand and manipulate the complex interplay between dispersion, local resonances, and dissipation. The dispersion and resonance properties of a damped metamaterial may be controlled by changing the levels of dissipation, and, conversely, it is possible to enhance, or reduce, dissipation by engineering the dispersion properties.

The objective of this thesis is to advance the understanding of the connection between dispersion, local resonances, and dissipation in viscoelastically damped metamaterials and to develop a methodology for precise engineering of the dissipation. A viscoelastic damping model is fitted with experimental data for accurate prediction of dissipation within the dispersion and finite-structure analysis frameworks. An intriguing phenomenon that is investigated using this modeling framework is metadamping–--a dissipation emergence phenomenon caused by the presence of local resonances. This concept is investigated in a real-world system, both numerically and experimentally. A methodology is developed to determine the levels of dissipation in a finite metamaterial pillared beam structure using only unit-cell analysis. With this information, guidelines are provided that enable engineering of the dissipation by varying the unit-cell dispersion properties. Results show that dissipation can either be enhanced, or reduced, within prescribed frequency ranges without sacrificing stiffness. This concept is first shown in the context of freely propagating waves and then extended to harmonically driven waves.

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