Dynamic characteristics of viscoelastic nanoplates under moving load embedded within visco-Pasternak substrate and hygrothermal environment

This research is focused on the size-dependent dynamic deflections of viscoelastic orthotropic nanoplates under moving load embedded within visco-Pasternak substrate and hygrothermal environment. The size-dependent effect is taken into account by employing nonlocal elasticity theory. Based on the classical plate theory, the size-dependent equations of motion are derived by employing Hamilton's principle. The size-dependent dynamic responses of simply supported nanoplates are solved based on Navier solution and state-space methods. The effects of applied loads, nonlocal parameter, substrate and hygrothermal environment on the frequency, critical velocity and transverse deflection of single layer graphene sheets are studied in detail.