Vibration analysis of 2D-functionally graded nanobeams using the nonlocal theory and meshless method

摘要

In this study a formulation based on the meshless method is developed to study the dynamic behavior of 2D-functionally graded nanobeams. The First order shear deformation theory is employed to model the behavior of the functionally graded beam and the small size effect is considered by employing the nonlocal theory of elasticity. The material properties are functionally graded both in the thickness and length of the nanobeam. The governing equations of the 2D-FG nanobeam are derived based on the Hamilton's principle. A meshless formulation based on the weak form of the governing equations and the point interpolation method with radial basis function is derived for discretization and solution of the problem and the mathematical details are presented. The convergence of predictions is investigated, and the predictions of presented solution are validated by comparing with the available results in the literature for special cases, and good agreements are achieved. Various numerical results are presented and the emphasis is placed on investigating the effect of several parameters such as small scale effects, the material distribution profile, mode number, length to thickness ratio and boundary conditions on the normalized natural frequencies of 1D- and 2D-FG nanobeams.