Session: Government Agency Student Posters

Paper Number: 173414

Band Gap Closing and Emergence of Non-Dispersive Wave Behavior in Phononic Crystals With Harmonically-Graded Elastic Profiles 

Metamaterials are architected materials with tailored microstructures that have revolutionized control over wave propagation, enabling new phenomena in wave guidance, steering, and attenuation that are not feasible in homogenous structures. Significant among these are phononic crystals (PnCs) which represent a class of engineered composites with a periodic arrangement of layers that repeat themselves in space. In conventional PnCs, these self-repeating blocks, also known as unit cells, typically consist of distinct materials with contrasting inertial and elastic properties. For example, a combination of a hard and a soft material is the simplest way to construct a bi-layered PnC unit cell. These arrangements give rise to band gaps which are wide frequency ranges within which wave propagation is forbidden. In conventional PnCs, band gaps are well understood as a direct outcome of impedance mismatches between the neighboring layers which culminate in Bragg scattering and cancelation along the wave propagation direction. Phononic band gaps are a hallmark feature of PnCs which have been strategically deployed in numerous applications over the past three decades, ranging from frequency-selective vibrational filters to topological insulators and mechanical diodes.

In this work, we focus on a less-commonly studied configuration of PnCs in which the unit cell is formed via a continuous variation of material properties as opposed to distinct layers of contrasting materials. While structures having a composition that follows a prescribed pattern or mathematical function, also known as functionally graded materials (FGMs), have been widely adopted for several applications, their study in the context of wave manipulation is scarce. In here, we investigate a set of novel wave phenomena in one-dimensional (1D) PnCs that are comprised of slender rods subject to longitudinal vibrations, where the elastic modulus follows a harmonic profile. While conventional (multi-layered) PnC rods are known to exhibit an infinite number of phononic band gaps, an elastically-graded PnC only reveals a single, well‐defined band gap that can be tuned by varying the parameters of the harmonically-varying stiffness. More interestingly, the wave response of this system shows a cut-off frequency above which the structure, although periodic in nature, retains a fully non-dispersive behavior which is analogous to a homogenous (single-material) rod with a constant wave speed. While intriguing, the above phenomena only emerge in PnCs with a true harmonic variation of stiffness, i.e., one that follows a continuous mathematical function and is modeled analytically without numerical discretization into a finite number of distinct layers. Upon discretization, the closed band gaps gradually open and the suppressed non-dispersive behavior at higher frequencies is restored. Understandably, as the resolution of the discretized harmonic profile increases, the behaviors of the continuous and discretized systems approach one another. While a few studies have aimed to utilize functionally graded PnCs, they predominantly focus on changing band gap width along the frequency axis by employing numerical simulations and iterative methods, resulting in limited design rules for specific configurations which cannot be generalized. In here, we seek to understand this transition both in terms of closing of higher frequency band gaps and loss of dispersive scattering in the PnC medium, in a manner which provides physical insights, is broadly applicable, and provides a generalized framework. We employ a segmented discretization of the harmonic profile to approximate its continuous form with the goal of deriving a semi-analytical solution that systematically captures how the number of segments govern the emergence, width, and eventual closure of the band gaps. By varying the resolution of discretization, we gain valuable insight into the changes in band gap widths and the subsequent morphing of the dispersion bands, which enables the design of broadband vibrational isolators with tailored and reconfigurable frequency filtering capabilities.

Presenting Author: Md Fuad University at Buffalo (SUNY)

Presenting Author Biography: Md Fuad (Zarif) is a senior in the Mechanical and Aerospace Engineering department at the University at Buffalo (SUNY). He completed his NSF-sponsored REU at the Sound and Vibrations Laboratory in the summer of 2025. He has been on the Dean's list 5 times during his undergraduate tenure. He is also a recipient of the "Pride of NY" scholarship.

Authors:

Md Fuad University at Buffalo (SUNY)
Ali Jafari University at Buffalo (SUNY)
Karim Soliman University at Buffalo (SUNY)
Hosam Yousef University at Buffalo (SUNY)
Tarunraj Singh University at Buffalo (SUNY)
Mostafa Nouh University at Buffalo (SUNY)