Nonlocal elasticity effect on Linear Axisymmetric Vibration of Nano-disks using Adomian decomposition method

In this study, the small scale effect on the linear free-field vibration of a Nano-disk has been investigated using Nonlocal elasticity theory. The formulation is based on the classical theory and the linear strain in cylindrical coordinates. To take into account the small scale and the linear geometric effect, the governing differential equation based on nonlocal elasticity theory, was extracted from Hamilton principle while the inertial effect as well as the shear stresses effect were ignored. Effect of nonlocal parameter is investigated by solving the governing equation using Adomian decomposition method for clamped and simply supported boundary conditions. Present nonlocal elasticity solutions show that the natural frequency decreases with increase in nonlocal parameter. For comparison, the linear equations were solved by the analytical method. A very good agreement was observed between the two methods. This indicates that the latter method can be applied for linear solution of Nano-disks with a high accuracy while simplifying the problem.

Keywords:

Linear free vibration , Nano-disks , Nonlocal elasticity , Adomian decomposition method