Application of the energy balance method to nonlinear vibrating equations

Nonlinear oscillation of nanoelectro-mechanical resonators using energy balance method: considering the size effect and the van der Waals force

“…The energy balance method utilizes the advantage of this point to collocate a solution at h = p/4. More details of the energy balance method can be found in Mehdipour et al (2010). Following the energy balance method, the variational principle of Eq.…”

“…Now, the following trial function is assumed to determine the angular frequency of the system (x) (Mehdipour et al 2010):…”

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.…”

An extended harmonic balance method based on incremental nonlinear control parameters

“…The Max-min [6], the parameter-expanding approach [7], frequency-amplitude formulation [8], the Variational Iteration [9], perturbation techniques [10,11,12], the iteration perturbation [13], the Homotopy Analysis [14,15], the Energy Balance analysis [16], the harmonic balance [17], the equivalent linearization method (ELM) [18,19] and 20 the Extended Lindstedt-Poincare approach [20] are some examples of these techniques. Each of these methods has some strong points and some weakness.…”