Estimated the frequencies of a coupled damped nonlinear oscillator with the non-Perturbative method

The current article is concerned with a comprehensive investigation of achieving the simplest solution of non-conservative coupled nonlinear forced oscillators. The article mainly depends on a non-perturbative method. It depends on yielding an equivalent linear system. The advantage of this linear system is that its coefficients are easily computed and that they include the effects of the original nonlinear coefficients. This linearization approach allows achieving quasi-exact solutions even in the presence of periodic forces. The relationships of frequencies with amplitudes are easily established. The analytical solution so yielded may serve as a basis for a qualitative understanding of the actual behavior of the coupled nonlinear oscillators. Additionally, numerical calculations are carried out graphically to address the validation of the new approach and to further illustrate the effectiveness and convenience of the method. The results are compared with the exact numerical solutions which show perfect accuracy. The method can be easily extended to other nonlinear systems and can therefore be exceedingly applicable in engineering and other sciences.

Automated summary

This article presents a comprehensive investigation of achieving the simplest solution for non-conservative coupled nonlinear forced oscillators. A non-perturbative method is employed to establish an equivalent linear system, which allows for quasi-exact solutions and easy determination of frequency-amplitude relationships. The approach is validated through numerical calculations and shows perfect accuracy when compared with exact numerical solutions. The method has wide applicability in engineering and other sciences.