Dispersion Analysis of Nonlocal Elastic Waves in Thin Plates: Nonlocal Elastic Waves Dispersion in Thin Plates

Abstract

This research investigates the propagation of elastic waves in uniform thin plates using the framework of nonlocal elasticity theory. Focusing on plates with stress-free boundary surfaces, the study derives and analyses two distinct dispersion relations corresponding to symmetrical and antisymmetrical wave modes with respect to the plate’s mid-plane. Owing to this symmetry, the plate can effectively be treated as two identical halves, which simplifies the mathematical analysis while preserving the essential physical behaviour of the system. The study further examines the influence of the nonlocality parameter on the dispersion characteristics of both wave modes, showing that small-scale effects significantly modify wave propagation compared with predictions from classical elasticity theory. In addition to the general formulation, the paper also considers several limiting cases to validate the model and clarify its physical implications under special conditions. Numerical computations and graphical illustrations are included to provide a clearer picture of how nonlocal effects alter wave behaviour, emphasizing their specific role in shaping the dispersion response of thin plate structures.