Application of He's Energy Balance Method to a Nonlinear Oscillator with Discontinuity

He’s frequency formulation for nonlinear oscillators using a golden mean location

“…This equation can be solved by the energy balance method [16][17][18], the parameter-expansion method [19], and the homotopy perturbation method [20].…”

A simple approach to nonlinear oscillators

“…Recently many effective methods were suggested to solve nonlinear oscillators, such as the variational iteration method [1], the homotopy perturbation method [2], the parameter-expansion method [3], energy balance method [4], harmonic balance method [5], a complete review on various analytical methods is available in Refs. [6,7].…”

More accurate approximate analytical solution of pendulum with rotating support

“…Iterative homotopy harmonic balance (Guo and Leung, 2010), differential transformation (Ghafoori et al, 2011) and max-min (Yazdi et al, 2012) methods have been developed for solving strongly nonlinear oscillators. Energy balance method (He, 2002;Khan and Mirzabeigy, 2014;Alam et al, 2016;Mehdipour et al, 2010;Ebru et al, 2016;Zhang et al, 2009) is another widely used technique for solving strongly nonlinear oscillators. Though, all these analytical methods have been developed for handling nonlinear oscillator, they provide almost similar results for a particular approximation.…”