Nonlinear Vibration Analysis of Nano-disks Based on Nonlocal elasticity Theory Using Homotopy Perturbation method

In this study, the small scale effect on the nonlinear free-field vibration of a nano-disk has been investigatedusing Nonlocal elasticity theory. The formulation is based on the classical theory and the non-linear model of Von Karmanstrain in cylindrical coordinates. To take into account the small scale and the nonlinear geometric effect, the differentialequation governing the Nonlocal elasticity theory, was extracted from Hamilton principle while the inertial effect as wellas the shear stresses effect were ignored. The equation of motion was discretized using Galerkin method and selection ofappropriate function based on the boundary condition defined for the nano-disk. Due to presence of nonlinear terms, theHomotopy perturbation method (HPM) was used to solve the discreted equations. A combination of Homotopy andperturbation methods was used to ease up the solution and completely solve the problem. For further comparison, thenonlinear equations were solved by the fourth order Runge-Kutta method; the solution of which was compared with thatof Homotopy Perturbation method. A very good agreement was observed between the two methods. This indicates that thelatter method can be applied for nonlinear solution of nano-disks with a high accuracy while simplifying the problem.

کلیدواژه ها:

Nonlinear free vibration ، Nano-disks ، Nonlocal elasticity ، Homotopy perturbationmethod