A new perspective on the dynamic forced 2-DOF system with the non-perturbative approach

An elegant and straightforward method based on the equivalent linearized method is offered for the analysis of nonlinear vibrations of forced 2-DOF dynamical systems, in search of a simple good approximate solution with the non-perturbative approach. In the present approach, the 2-DOF system is transformed into a decoupled linear oscillator with instantaneous frequency identification. In this approach, we avoid the restriction on the periodic force coefficient, which was considered to be well below unity in various perturbation methods. This liberation of the amplitude of the periodic force led to the emergence of new patterns of the formation of periodic solution waves. It is found that the existence of the periodic force has an inhibitory effect on the scattering factors unless their frequency approaches the natural frequency of the dynamic system. The validation of the scheme is shown by comparing the numerical findings with the existing results. The supremacy of the proposed scheme is demonstrated by making numerical comparisons for each pattern of the obtained solution. The analytical solutions show high consistency proving the accuracy of the non-perturbative approach. This motivates us to extend the scheme for solving free and forced nonlinear vibrations of more coupled structures. It is noteworthy as a new technique with significant usefulness.