Vibration of nano-disks using Adomian decomposition method based on nonlocal Mindlin plate theory

In this study, the small-scale effect on the linear free-field vibration of a nano-disk has been investigated using the Nonlocal elasticity theory. The formulation is based on the Mindlin plate theory(first-order shear deformation)and the linear strain in cylindrical coordinates. To take into account the small scale effect, the governing differential equation was extracted based on nonlocal elasticity theory, using the Hamilton principle, while the inertial and shear stress effects were considered. The effect of nonlocal parameter is also investigated on the vibrational modes and frequencies by solving the governing equation using the Adomian decomposition method for the two clamped and simply supported boundary conditions. Present nonlocal elasticity solutions show that the natural frequencies decrease with an increase in the nonlocal parameter. For comparison and versatility manifestation of the Adomian decomposition method in the solution of such problems, the linear equations were solved by the analytical method. Very good agreements were observed between the results of both methods. This shows the versatility of the latter method in obtaining high accuracy and considerable simplification in the solution of vibrational problems concerned with the nano-disks.

کلیدواژه ها:

Linear free vibration ، Mindlin plate Theory ، Nano-disks ، Nonlocal elasticity ، Adomian decomposition method.