Investigating the influence of higher-order boundary conditions on free vibrations of bi-directional FG thick conical micro-shells

The present paper investigates the influence of higher-order boundary conditions caused by accounting the small scales effect on free vibrations of bi-directional functionally graded thick conical micro-shells. The present model accounts for the gradation of the material length scale parameter as one of the micro-shell mechanical properties along its thickness as well as its axial axis. The modified couple stress as well as the first-order shear deformable love shell theories together with the Ritz method are employed to obtain the eigenvalue eigenvector equations governing on the free vibrations of the micro-structure. These equations are solved for some different types of boundary conditions. The present findings are compared and successfully validated by the available results in the literature. The influences of small scales, higher-order boundary conditions and power law distribution indices in both the transversal and axial directions on free vibrations of conical micro-shells are then investigated. The results reveal that higher-order boundary conditions play a crucial role in dynamics of conical micro-shells especially when these boundary conditions directly affect the eigenmodes which are dominant in the dynamics of the structure. In addition, it is observed that although the dynamics of the present conical micro-shell is affected by the power law distribution indices in both the transversal and axial directions, it is more sensitive to the transversal one.