Homotopy Perturbation Method for the Attachment Oscillator Arising in Nanotechnology

Bubble electrospinning is an effective method to produce nanofibers with different morphologies. Numerous polymer film fragments are formed from bursting bubbles, which elongate to nanofibers under high electrostatic voltage. In two polymers, bubble electrospinning film fragments of both polymers could interact due to the dominant surface-induced force named geometrical potential. Mathematical models are established to elaborate on the non-linear oscillators with singular terms. Parameter expansion technology used in the homotopy perturbation method can be useful for such kind of non-linear oscillators. In this paper, this technique is implemented to find the amplitude-frequency relationship of the attachment oscillator used in the molecular electrospinning process to produce nanofibers. The results depict the effectiveness of the method and show that the frequency obtained for duffing oscillator is highly accurate in exceptional cases.