Vibration analysis of graphene platelet reinforced stadium architectural roof shells subjected to large deflection

In the present work, the vibration characteristics of sandwich nanocomposite shells, fortified with graphene platelets (GPLs) have been researched. The shell has been considered as the stadium roof shape with double curvatures under vibration due to earthquake. The nanocomposite has the matrix of concrete which is fortified with uniform or linear dispersions of GPLs. Also, the core possesses cellular type square architecture for which the effective elastic modulus has been defined in the context of relative density based relations. Based upon the classic shell strains containing two identical curvatures, the governing equations have been established and solved through differential quadrature approach. It will be seen that the vibrational frequencies rely on the core relative density, height of layers, the amount and dispersions of GPLs and even shell geometric parameters.