Surface Bloch Waves in Phononic Crystals: Theory, Manipulation, and Applications to Non-Destructive Evaluation

About This Grant

Phononic crystals are engineered materials with repeating internal structures that allow for the control and manipulation of sound and vibration in ways that go beyond traditional materials. These structures have a wide range of applications, including vibration control, noise reduction, energy harvesting, sensing, and communication technologies. However, a major challenge limits their practical deployment: when these materials are manufactured as real, finite components, as opposed to idealized, infinite structures, surface waves develop along their boundaries that are poorly understood and difficult to predict. The research funded by this award seeks to bridge a critical gap in scientific understanding by creating a new theoretical framework to describe, manipulate and ultimately harness the sensing potential of surface waves in phononic crystals. This project serves the national interest by advancing non-destructive evaluation techniques for infrastructure safety and aerospace applications, improving quality control of next-generation composite materials, and enabling more efficient acoustic devices for medical diagnostics. The project will also support workforce development by training graduate students in advanced computational and experimental methods, while generating fundamental insights that will benefit a broad scientific community working in wave physics, material characterization, and additive manufacturing. Building on preliminary work focused on scalar waves, this research aims to establish a comprehensive framework for analyzing, controlling, and harnessing surface-bound waves in phononic crystals through three interconnected objectives. First, the mathematical concept of surface Bloch waves will be formulated as the boundary layers native to traction-free surfaces of phononic crystals, which will lead to the development of a unit-cell-based, reduced-order model that predicts their dispersion, waveforms, power flow, and spatial decay (or “skin depth”). Second, this research will explore how engineered geometric design of the traction-free surfaces, through controlled orientation, elevation, and periodic undulation of surface cuts, can be leveraged to manipulate the surface Bloch waves. The reduced-order model will support efficient parametric exploration of the geometric design space. Third, an experimental study using laser Doppler vibrometry will be conducted to (i) verify the theoretical framework, and (ii) develop a non-destructive evaluation methodology that extends widely used spectral-analysis-of-surface-waves (SASW) technique to as-fabricated phononic crystals. This project is expected to yield new insights into the physics of surface waves and boundary layers in periodic media, while delivering practical tools for inverse characterization of additively manufactured phononic crystals. This study seeks to create the foundational knowledge enabling further exploration of interfacial wave phenomena and topological effects in structured solids. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.