چكيده به لاتين
As the macroscale structures in the form of plates have many applications in nanoscale are particularly important. For this reason, the study of vibrating behavior of nanoplates is one of the most important factors for designing these structures. In this thesis, an exact analytical approach of the free vibrations of circular FGM nanoplates in the presence of surface effects including surface elasticity, surface tension, and surface density is presented. Also, the balance conditions between FGM nanoplate bulk and its surfaces are considered to be satisfied assuming a cubic variation for the component of the normal stress through the FGM nanoplate thickness. It should be noted that Kirchhoff and Mindlin plate theories are upsized to modeling the thin and moderately thick plates, respectively. Hamilton’s principle is used to derive the equations of motion and natural boundary conditions of the nanoplate, and the new potential functions are employed to exactly decouple the governing equations. The properties of nanoplate are graded in the thickness direction according to a volume fraction power-law distribution whereas Poison’s ratio is set to be constant.
In order to verify the reliability of the method considered, the results are compared with those presented in the literature. Finally, the effects of various parameters such as a radius of the nanoplate, thickness to radius ratio, boundary conditions, material properties, and mode number on the natural frequencies are investigated.
