Date of Award
Doctor of Philosophy (PhD)
Aerospace Engineering Sciences
Mahmoud I. Hussein
Carlos A. Felippa
Through deliberate material and geometrical design of the internal structure, phononic crystals and metamaterials, collectively, phononic materials, elicit fundamental wave phenomena pertaining to acoustic/elastic systems. This unique ability among classical materials and composites has immediate engineering applications including vibration control in structures. Moreover, ongoing research has been directed toward technological improvements in communications, energy harvesting, and acoustic imaging as well as the proposal of new devices for acoustic cloaking, nondestructive super-resolution imaging, and even flow control. Periodicity, emerging from the spatial repetition of a representative structural element, the unit cell, is a characteristic feature of phononic materials and makes them accessible to Bloch's theorem for dynamic analysis. This analysis is central to predicting phononic material performance which inspires the previously stated applications. However, energy dissipation stemming from the damping mechanisms inherent to all materials is absent from much of the theoretical literature. This omission adversely affects the prediction of phononic material performance and foregoes damping as a potential design parameter/objective. In support of improved performance predictability and strategic material design with damping, this dissertation extends the analysis techniques originally developed in the context of dissipative vibration in damped structures to dissipative wave propagation in damped phononic materials.
The frequency band diagram summarizes much of the dynamic performance of phononic materials and, ultimately, phononic devices, visually separating propagating and non-propagating wave modes into distinct frequency regions denoted pass bands and band gaps, respectively. Accounting for the practical effects of energy dissipation on the acoustic/elastic waves improves the predictive capability of the band diagram and is one of the main thrusts of this dissertation. Both the material and excitation environment are considered. Viscous and viscoelastic type damping, respectively, represent dissipation consistent with motion involving a fluid and the time-dependent behavior of polymers and metals. The dissertation shows the changes that occur in the band diagram, especially the size of the band-gap region, as the damping is tuned continuously from one damping type to another. Regarding the excitation environment, phononic structures may be subject to impact and harmonic loading. The dissertation investigates the distinctive response of free and prescribed waves to energy dissipation, with implications for phononic structures subject to impact and harmonic loading, respectively. Free waves dissipate energy over time while prescribed waves dissipate energy over the extent of phononic material/structure producing radically differing band diagrams for the same phononic material.
For cloaking and super-resolution imaging devices, performance is further linked to the properties of the underlying phononic material. No natural material or composite exhibits the negative density/modulus or anisotropic density required for their operation. However, over a narrow range of wave frequencies, these extraordinary properties emerge dynamically in phononic materials due to relative motion among the internal structure. This dissertation advances the discussion of phononic material performance by examining the changes undergone by the dynamic effective properties due to energy dissipation. In addition to the conventional dynamic effective density and modulus, a dynamic effective viscous damping constant is presented and provides a means of measuring damping beyond the low-frequency regime of the viscoelastic correspondence principle.
As an additional focus, this dissertation also considers damping as an objective of phononic material design. The results of the previous studies, in particular, that on free wave propagation in damped phononic materials, opened the door to design proposal for enhanced dissipation. The dissertation examines the effect of phononic material configuration on the overall material damping capacity, demonstrating the emergence of enhanced dissipation in phononic materials featuring localized resonating bodies as compared to those without. Such behavior, which in our work has been referred to as "metadamping", provides a new strategy for the design of material systems that exhibit high levels of dissipation without sacrificing load-bearing capacity (stiffness) which is a feat beyond most traditional materials and composites.
Frazier, Michael Joseph, "Dissipative Wave Propagation in Phononic Crystals and Metamaterials: Models and Analysis" (2015). Aerospace Engineering Sciences Graduate Theses & Dissertations. 112.