Analytical approximate technique for strongly nonlinear oscillators problem arising in engineering

In this paper, a novel method called generalized of the variational iteration method is presented to obtain an approximate analytical solution for strong nonlinear oscillators problem associated in engineering phenomena. This approach resulted in the frequency of the motion as a function of the amplitude of oscillation. It is determined that the method works very well for the whole range of parameters and an excellent agreement is demonstrated and discussed between the approximate frequencies and the exact one. The most significant features of this method are its simplicity and excellent accuracy for the whole range of oscillation amplitude values. Also, the results reveal that this technique is very effective and convenient for solving conservative oscillatory systems with complex nonlinearities. Results obtained by the proposed method are compared with Energy Balance Method (EBM) and exact solution showed that, contrary to EBM, simply one or two iterations are enough for obtaining highly accurate results.