Wave dispersion in nonlocal anisotropic macro/nanoplates made of functionally graded materials

Abstract

By means of a higher-order shear deformation theory (HSDT) coupled with the nonlocal elasticity theory, this work is attempted to elucidate the size-dependent behavior of functionally graded (FG) Anisotropic macro/nanoplates. In the HSDT, the displacement field is modeled as a combination of an exponential formula and a trigonometric function. This type of theory has only five unknowns but can have precise results in various conditions for thick and thin plates. By employing Hamilton’s principle, the governing equations are derived for FG anisotropic macro/nanoplates. In the case of FG anisotropic materials, all components of elastic stiffness tensor are involved, and the material gradation is considered to be arbitrary in the thickness direction. In order to attain the analytical dispersion relations, an eigenvalue problem is solved. The model’s validation is evaluated by comparing authors’ results with other papers available in the open literature. The influences of nonlocal parameter, exponential factor, geometrical shape, and wave number on the circular frequencies and phase velocities are inspected. From the knowledge of authors, it is the first time that the small-scale influences for FG anisotropic macro/nanoplates based on the present higher-order shear deformation theory are investigated.