Free axial vibration of Rayleigh nanorods based on nonlocal elasticity theory

A great majority of studies, supports were identified as known special conditions. These boundary conditions cannot be applied in real life. So, in this study, supports of microbeams were chosen as strings. A main purpose of this study is obtaining an equation which can be applied for all boundary conditions when we changed values for strings. In line with this purpose, first free axial vibration of Rayleigh nanorods which were supported by strings was analysed and effects of parameters to values of vibrations were observed. Later axial static analysis of an axial loaded fixed cantilever microbeam was done. Weighted residuals methods were used in this study. These methods are Galerkin, subdomain, least squares and two parameters. In last part of study, bending analysis of a triangular distributed loaded fixed cantilever microbeam was done with using same weighted residuals methods. Consequently, an equation can be found for all different boundary conditions when strings were used.