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