Dynamics research of Fangzhu’s nanoscale surface

In this paper, we mainly focus on a fractal model of Fangzhu’s nanoscale surface for water collection which is established through He’s derivative. Based the two-scale transform method, approximate analytical solutions are obtained by energy balance method and frequency–amplitude formulation with average residuals. Some specific numerical experiments show that these two methods simple effective can be adopted to other nonlinear oscillators. addition, properties solution reveal how enhance rate Fangzhu adjusting smoothness its surfaces.