Abstract
Based on the energy balance method (EBM), a more accurate analytical solution of the pendulum equation with rotating support was presented. The results were compared with those obtained by the differential transformation method (DTM) and He’s improved energy balance method. It was shown that the results are more accurate than the said methods. Key words: Energy balance method, approximate solutions, nonlinear oscillators, pendulum with rotating support.
Highlights
Many scientific problems in natural sciences and engineering are inherently nonlinear, but it is difficult to determine their exact solutions
energy balance method (EBM) has been modified by truncating some higher order terms of the algebraic equations of related variables to the solution (Alam et al, 2016) and it measures more correct result than the usual method
The EBM (Alam et al, 2016) was utilized to determine the approximate solution of pendulum equation with rotating support. This type of oscillator was analyzed by Ghafoori et al (2011) applying differential transformation method (DTM), Belendez et al (2006) using harmonic balance method and Yazdi et al (2012) using max-min approach. He (2002) first introduced energy balance method and Khan and Mirzabeigy (2014) was used to improve accuracy of He’s energy balance method to obtain the solution of pendulum equation with rotating support
Summary
Many scientific problems in natural sciences and engineering are inherently nonlinear, but it is difficult to determine their exact solutions. 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.
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