Effect of Rotary Inertia on Vibrational Response of Embedded Graphene Sheets

Abstract

In the present study, influence of rotary inertia on the size-dependent free vibration analysis of embedded single-layered graphene sheets is examined based on modified couple stress theory. Governing differential equations and corresponding boundary conditions in motion are derived by implementing Hamilton’s principle on the basis of Kirchhoff thin plate theory. Also, effect of elastic foundation is taken into consideration by using a two-parameter elastic foundation model. Influences of additional material length scale parameter, mode number, elastic foundation and rotary inertia on the natural frequencies are investigated in detail.