Analytical solution for strongly nonlinear oscillation systems using energy balance method

This paper applied He’s energy balance method (EBM) to solve the non-natural vibrations and oscillations. We find that this method (EBM) works very well for the whole range of initial amplitudes and does not demand small perturbation and also sufficiently accurate to both linear and nonlinear physics and engineering problems. We consider a high nonlinear single degree of freedom to illustrate the effectiveness and convenience of the method. He’s energy balance method as approximate method and Runge-Kutta’s (RK) algorithm was also implemented to solve the governing equation through a numerical method. Finally, the accuracy of the solution obtained by the approximate method (EBM) has been shown graphically and compared with that of the numerical solution.   Key words: Energy balance method, nonlinear oscillators, mathematical pendulum, Runge-Kutta’s algorithm.

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