Fractional Derivative Analysis of Wave Propagation Studies Using Eringen's Nonlocal Model with Elastic Medium Support

Purpose The present work aims to study the phase speed and group speed of Eringen's nonlocal model for one-dimensional structures using the fractional derivatives approach (Challamel et al. in C R Mec 341:298-303, 2013). The present investigation includes the explicit expression derivation of group speed in a concise form for the first time. Methodology The Caputo fractional derivative approach helps in transforming the classical Eringen's nonlocal model into the fractional model. For the first time, the elastic medium support influences the Caputo fractional model to study its effects on wave propagation study. Conclusion The Caputo fractional model's phase speed and group speed predict better results than classical Eringen's nonlocal model examining Born-Karman results as a benchmark in the absence of elastic medium support. The increase in elastic medium effects increases the frequencies and phase speed. Interestingly, the group speed decreases with the rise in elastic medium constant values.