FORCED NONLINEAR OSCILLATOR IN A FRACTAL SPACE

A critical hurdle of a nonlinear vibration system in fractal space is the inefficiency modelling system. Specifically, differential equation models cannot elucidate effect porosity size and distribution periodic property. This paper establishes fractal-differential model for this purpose, Duffing-Van der Pol oscillator (DVdP) with two-scale derivatives forced term considered as an example to reveal basic properties oscillator. Utilizing transforms He-Laplace method, analytic approximate solution may be attained. Unfortunately, not physically preferred. It has modified along frequency analysis, stability criterion under consideration obtained. On other hand, linearized theory employed autonomous arrangement. Consequently, phase portraits around equilibrium points are sketched. For non-autonomous organization, criteria analyzed via multiple time scales technique. Numerical estimations designed confirm graphically analytical solutions well configuration. revealed that exciting external force parameter plays destabilizing role. Furthermore, both excited stiffness parameter, execute dual role picture.