Analytical Solutions in a First-order Cubic Nonlinear System with Periodically Forced Oscillator. Issue 1 (April 2021) - Sun, Danping; Chen, Lanzheng; Wan, Renzhuo; Zhou, Guopeng
Abstract: In this paper, the analytical solutions for the period-1 motion of a cubic nonlinear dynamical system with two periodic forced terms are obtained through the generalized harmonic balance method. From the method, the analytical solutions are transformed to the Fourier series expansion in all harmonic terms at the equilibrium position. The stability and bifurcation analysis are investigated through eigenvalues analysis, and the accuracy of the analytical solutions is verified by numerical simulations. The harmonic amplitude distributions are presented to show the characteristic of the different-order terms with different excitation frequencies. From this study, the system parameters that make the system stable are determined. Furthermore, the robustness of the system is guaranteed by selecting the parameters appropriately.