Vibrations of Arbitrary Thick and Deep Nanocomposite Curved Beams Using a Novel Improved Shear and Normal Deformable Model.

In this research, the equations governing the vibrations of a composite curved beam reinforced with graphene platelets have been solved using a quasi-3D model of the beam. The investigated composite beam is multi-layered, each layer can be reinforced by different amount of graphene platelets, which leads to a functionally-graded distribution of reinforcements. According to the quasi-three-dimensional theory of beams, the effect of thickness stretching and shear strains is included and does not require a shear correction factor. It should be noted that according to the geometry of the assumed beam, deformations and strains are considered small and the structural relations of the material are linear. The governing equations of the curved beam are derived based on Hamilton’s principle after calculating the kinetic and strain energies. The boundary conditions of the beam are assumed to be simply supported on both ends. Therefore, the displacement parameters of the problem have been explained with Navier’s solution method and with the use of Fourier expansions, closed form expressions are obtained as elements of mass and stiffness matrices. The elasticity modulus of the beam is rewritten using the Halpin–Tsai model and Poisson’s ratio and mass density using the rule of mixtures. Finally, the results of each section are presented in the form of tables. First, the results of this research were verified with the existing results, and then new results were introduced to investigate the effective parameters of the problem. These results include the investigation of the distribution of graphene platelets, the effect of the weight percentage of the filler and the geometric properties of the beam. The results of this research on the dynamic response of the beam show that the effects of increasing the volume percentage of graphene, even to a small extent, can be seen in increasing the natural frequency of the curved beam. [ABSTRACT FROM AUTHOR]