Session: 01-02-03: Phononic Crystals and Metamaterials

Paper Number: 150801

150801 - Designing Elastic Lattices by Applying Principles From Cellular Automaton 

For a few decades, periodic lattices have been the focus of extensive research due to their unique vibrational properties. Unlike naturally occurring materials and composites, periodic lattices enable unique phenomena in acoustic and elastic media, such as frequency bandgaps (i.e., frequency ranges of blocked wave propagation), negative inertia and/or stiffness, and high refractive indices. These properties have led to applications in vibration and noise control, flow stabilization, acoustic logic gates, energy harvesting, cloaking, wave guiding, topological protection, and non-reciprocal and asymmetric wave transmission. However, certain types of aperiodic lattices have opened up possibilities for new phenomena that are not achievable with periodic structures. For instance, quasi-periodicity is essential for a certain type of topologically protected edge states with various localized edge modes to manifest themselves. Additionally, topological pumping—a process where a two-dimensional (aperiodic) structure is adiabatically modulated to gradually transfer a signal from one corner to the opposite—has been both experimentally and theoretically demonstrated. Similarly, rainbow trapping, achieved through an array of resonators with non-periodic system parameter changes, has been utilized for vibration isolation and energy harvesting.

Inspired by the potential of uniquely designed lattices that are not necessarily periodic and the need for innovative methods to control elastic and acoustic waves, I draw from Cellular Automaton (CA) principles to propose a novel class of lattice designs. Cellular Automaton, a discrete computation model developed by von Neumann in the 1950s, has been widely adopted across various fields due to its versatility, including biology, physics, statistical mechanics, fracture quantification, and design of piezoelectric patches. As an example, I introduce a lattice design based on the Ulam-Warburton Cellular Automaton (UWCA), named after its developers Ulam and Warburton. This algorithm creates aperiodic structures that follow defined rules, resulting in intriguing patterns. By applying UWCA principles to elastic lattices, starting from a square monatomic lattice, the resulting structures exhibit unique dynamical properties. These include symmetric eigenfrequency spectra, repeated natural frequencies of high multiplicity, and the emergence of strongly-localized corner modes, where the latter is dependent on the corners’ shape, which must be of a shape resembling a perpendicular-sign symbol.

Future research directions in this domain could involve exploring additional CA algorithms to develop unique elastic lattice designs and characteristics, in addition to studying their damping characteristics and effective elastic and inertial properties. It is anticipated that lattices inspired by computational algorithms may reveal new wave phenomena, potentially surpassing the capabilities of existing lattice designs.

Presenting Author: Hasan Al Ba'ba'a Union College

Presenting Author Biography: Dr. Al Ba’ba’a received his Ph.D. from the State University of New York at Buffalo (UB) in 2019, M.S. from University of Wisconsin – Milwaukee (UWM) in 2015, and B.S. from Hashemite University in 2010, all specializing in mechanical engineering. Following his Ph.D. graduation, Dr. Al Ba’ba’a held positions at multiple universities, such as part-time lecturer at Eastern Michigan University, Research Fellow in the University of Michigan, and Postdoctoral Associate at the University of Southern California and UB. Being a recipient of a competitive teaching fellowship during his Ph.D. studies, Dr. Al Ba’ba’a became very interested in leading an academic career that balances teaching and scholarship, which eventually led him to joining Union College in the Fall of 2022, where he is currently working as a visiting assistant professor of mechanical engineering.

Areas of research that Dr. Al Ba’ba’a is interested in are structural dynamics, wave propagation, and control theory, all with the aim of controlling and reducing mechanical vibrations in dynamical systems. Particularly, he investigates various classes of optimally engineered materials, such as elastic metamaterials and phononic crystals, to establish mathematical models for better understanding of their dynamical characteristics and consequently invent new classes of them. Dr. Al Ba’ba’a received multiple awards during his academic career, including the Chancellor’s Graduate Student Award by the College of Engineering and Applied Sciences at UWM, and the Dean’s Graduate Achievement Award at UB. In addition, his novel phononic pendula design for reducing vibrations in overhead cranes awarded second place in the Silent Hoist and Crane Co. Materials Handling Prize.

Authors:

Hasan Al Ba'ba'a Union College