Damping Characteristics of Nonlocal Strain Gradient Waves in Thermoviscoelastic Graphene Sheets Subjected to Nonlinear Substrate Effects

Abstract— The present study explores dispersion characteristics of thermal, viscoelastic and mechanical waves in graphene sheets subjected to uniform thermal loading and supported by the visco-Pasternak foundation. Kinematic relations for graphene sheets are deduced within two-variable refined higher-order plate theory. Damping effects of the viscoelastic medium are modeled using the Kelvin–Voigt model. The research extensively investigates the size-dependent behavior of graphene sheets by incorporating nonlocal strain gradient theory. Nonlocal governing equations are formulated under Hamilton’s principle and solved analytically to determine wave frequency values. To validate the results, a comparative analysis is conducted, and the outcomes are tabulated to confirm the effectiveness of the approach. Finally, graphical representations are employed to depict the influence of each parameter on the wave propagation responses of graphene sheets.