Nano-mechanical wave propagation in single-layer graphene sheets resting on elastic foundations: A memory dependent and nonlocal strain gradient approach

This analysis examines the nano-mechanical wave propagation response of a single-layer graphene sheet under plane-dependent bending strain and high-intensity impact loading. The sheet rests on an elastic medium, represented using a two-parameter foundation model. A two-variable trigonometric refined plate theory establishes the kinematic relationships, while a nonlocal strain gradient (NSGT) framework accounts for size-dependent behaviors. Memory effects are incorporated through the Memory Dependent Derivative (MDD) formulation. The governing equations are derived using Hamilton's principle, incorporating bending, impact, and memory influences. The resulting eigenvalue problem is solved analytically, and the roles of various parameters, including impact intensity and memory effects, are demonstrated through graphical results.