Nonlocal dynamic response of embedded single-layered graphene sheet via analytical approach

In the present research, static bending and dynamic responses of simply supported single-layered graphene sheet (SLGS) embedded in an elastic medium under uniform and sinusoidal loads are analytically investigated. The surrounding medium is simulated by visco-Pasternak model in which the damping and shearing effects are considered. Third-order shear deformation theory (TDST) is utilized because of its more accuracy relative to other plate theories. In order to consider size effects, nonlocal elasticity theory is employed. Applying Hamilton's principle, governing equations of the SLGS are obtained and solved using Fourier series-Laplace transforms method. Finally, the detailed parametric study is conducted to scrutinize the influences of small-scale parameter, elastic medium, length-to-thickness ratio and aspect ratio of nanoplate on the static and dynamic behaviours of SLGS. Results indicated that the surrounding medium has a significant effect on the static and dynamic response, so that, increasing shear constant and damping coefficients cause to decrease the deflection of SLGS, considerably. The result of this study can be useful to control and improve the performance of this kind of nano-mechanical systems.