This paper presents a comprehensive analysis of thermoelastic wave propagation in a single-layer graphene sheet on an elastic foundation, incorporating nanoscale-dependent mechanical effects. The model accounts for plane-dependent bending deformation and the influence of high-intensity impact loading on the graphene’s dynamic response. A two-parameter elastic foundation characterizes the sheet–substrate interaction, while the kinematics are described using a trigonometric refined plate theory. To capture small-scale effects, size-dependent constitutive relations are employed, and thermal relaxation is introduced via the Moore–Gibson–Thompson (MGT) thermoelastic model, enabling finite-speed heat transport. Memory effects are incorporated through the memory-dependent derivative (MDD), allowing a realistic description of nanoscale material behavior. Governing equations are derived using Hamilton’s principle, accounting for bending, impact loading, thermoelastic coupling, and foundation interaction. The resulting eigenvalue problem is analytically solved to obtain dispersion relations, and parametric studies examine the influence of impact intensity, memory parameters, thermal relaxation time, and foundation stiffness on wave propagation. The results reveal significant modifications in dispersion behavior due to combined thermal relaxation and memory effects, providing new insights into wave transport mechanisms in graphene nanostructures. These findings are expected to benefit the design and optimization of nanoelectromechanical systems, thermal actuators, and high-sensitivity sensing devices.
Selvamani et al. (Mon,) studied this question.