Nonlocal vibration analysis of circular double-layered graphene sheets resting on an elastic foundation subjected to thermal loading

Based on the nonlocal elasticity theory, the vibration behavior of circular double-layered graphene sheets(DLGSs) resting on the Winkler- and Pasternak-type elastic foundations in a thermal environment is investigated.The governing equation is derived on the basis of Eringen’s nonlocal elasticity and the classical plate theory(CLPT).The initial thermal loading is assumed to be due to a uniform temperature rise throughout the thickness direction. Using the generalized differential quadrature(GDQ)method and periodic differential operators in radial and circumferential directions, respectively, the governing equation is discretized. DLGSs with clamped and simply-supported boundary conditions are studied and the influence of van der Waals(vd W) interaction forces is taken into account.In the numerical results, the effects of various parameters such as elastic medium coefficients, radius-to-thickness ratio,thermal loading and nonlocal parameter are examined on both in-phase and anti-phase natural frequencies. The results show that the thermal load and elastic foundation respectively decreases and increases the fundamental frequencies of DLGSs.