Osama R. Bilal

Ultrawide phononic band gap for combined in-plane and out-of-plane waves.

We consider two-dimensional phononic crystals formed from silicon and voids, and present optimized unit-cell designs for (1) out-of-plane, (2) in-plane, and (3) combined out-of-plane and in-plane elastic wave propagation. To feasibly search through an excessively large design space (~10(40) possible realizations) we develop a specialized genetic algorithm and utilize it in conjunction with the reduced Bloch mode expansion method for fast band-structure calculations. Focusing on high-symmetry plain-strain square lattices, we report unit-cell designs exhibiting record values of normalized band-gap size for all three categories. For the case of combined polarizations, we reveal a design with a normalized band-gap size exceeding 60%.

Trampoline metamaterial: Local resonance enhancement by springboards

We investigate the dispersion characteristics of locally resonant elastic metamaterials formed by the erection of pillars on the solid regions in a plate patterned by a periodic array of holes. We show that these solid regions effectively act as springboards leading to an enhanced resonance behavior by the pillars when compared to the nominal case of pillars with no holes. This local resonance amplification phenomenon, which we define as the trampoline effect, is shown to cause subwavelength bandgaps to increase in size by up to a factor of 4. This outcome facilitates the utilization of subwavelength metamaterial properties over exceedingly broad frequency ranges.

Flow stabilization by subsurface phonons

The interaction between a fluid and a solid surface in relative motion represents a dynamical process that is central to the problem of laminar-to-turbulent transition (and consequent drag increase) for air, sea and land vehicles, as well as long-range pipelines. This problem may in principle be alleviated via a control stimulus designed to impede the generation and growth of instabilities inherent in the flow. Here, we show that phonon motion underneath a surface may be tuned to passively generate a spatio-temporal elastic deformation profile at the surface that counters these instabilities. We theoretically demonstrate this phenomenon and the underlying mechanism of frequency-dependent destructive interference of the unstable flow waves. The converse process of flow destabilization is illustrated as well. This approach provides a condensed-matter physics treatment to fluid–structure interaction and a new paradigm for flow control.

Topologically evolved photonic crystals: Breaking the world record in band gap size

Using topology optimization, a photonic crystal (PtC) unit cell can be designed to exhibit favorable electromagnetic wave propagation properties. Among these is the opening of a band gap (BG) with the largest possible ratio of width to midgap frequency. In this paper the aim is to maximize the relative size of the first and fourth relative BGs of two-dimensional (2D) PtCs with a square lattice configuration. In addition, we examine the effects of the degree of unit cell symmetry on the relative BG size and on the geometric traits of the optimized topologies. We use a specialized genetic algorithm (GA) for our search. The results show that the type of symmetry constraint imposed has a significant, and rather subtle, effect on the unit cell topology and BG size of the emerging optimal designs. In pursuit of record values of BG size, we report two low-symmetry unit cells as an outcome of our search efforts to date: one with a relative BG size of 46% for TE waves and the other with a relative BG size of 47% for TM waves.

Optimization of Phononic Crystals for the Simultaneous Attenuation of Out-of-Plane and In-Plane Waves

The topological distribution of the material phases inside the unit cell composing a phononic crystal has a significant effect on its dispersion characteristics. This topology can be engineered to produce application-specific requirements. In this paper, a specialized genetic-algorithm-based topology optimization methodology for the design of two-dimensional phononic crystals is presented. Specifically the target is the opening and maximization of band gap size for (i) out-of-plane waves, (ii) in-plane waves and (iii) both out-of-plane and in-plane waves simultaneously. The methodology as well as the resulting designs are presented.Copyright

Optimal Design of Periodic Timoshenko Beams using Genetic Algorithms

A periodic material is composed of two or more types of elastic materials laid out in space in a repeated periodic fashion. The properties of a periodic composite material depend on the arrangement of two or more materials within its unit cell. Periodic materials (also known as phononic materials) are commonly characterized by its dispersive frequency spectrum. With appropriate spatial distribution of the constituent material phases, spectral stop bands could be generated. Moreover, it is possible to control the number, the width, and the location of these bands within a frequency range of interest. This study aims at exploring the relationship between the unit cell conguration and its frequency spectrum characteristics. Focusing on 1D layered phononic materials (in the form of rods and beams), and longitudinal wave propagation in the direction normal to the layering, the unit cell features of interest are the number of layers and the material phase and relative thickness of each layer. An evolutionary search for multi-phase cell designs exhibiting a wide stop band, or a series of wide stop bands, is conducted using a specially formulated representation and set of operators that break the symmetries in the problem. Structures composed of the designed phononic materials are excellent candidates for use in a wide range of applications including the development of vibration and shock isolation structures, sound isolation pads/partitions, multiple band frequency lters, among many other applications.

A Fast Method for Electronic Band Structure Calculations

Band structure calculation provides a basis for the study of thermal, optical and magnetic properties of crystals. The reduced Bloch mode expansion (RBME) method is a model reduction method in which a selected set of Bloch eigenvectors within the irreducible Brillouin zone at high symmetry points are used to expand the unit cell problem at hand. In this method, a major reduction in computational cost is achieved with minimum loss of accuracy. The method applies to both classical and ab inito band structure calculations of periodic media, and to any type of wave propagation problem: phononic, photonic, electronic, etc. In this work, the applicability of RBME in calculating the three-dimensional (3D) electronic band structure for crystal structures with different symmetries is demonstrated. Using the Kronig-Penney fixed potential, a high-symmetry cubic model and a low-symmetry triclinic model are considered. For both cases, the energy (eigenvalues) and wave functions (eigenvectors) demonstrate very good convergence performance with the number of expansion points.Copyright