Periodic Solutions for Coupled Van Der Pol Oscillators of Three-Degree-of-Freedom Solved by Homotopy Analysis Method

In this paper, the homotopy analysis method is presented to establish the analytical approximate periodic solutions for three-degree-of-freedom (3DOF) coupled van der Pol oscillators. For given physical parameters of nonlinear systems, the frequency ω, displacements x₁(t), x₂(t) and x₃(t) can be explicitly obtained. In addition, comparisons are conducted between the results obtained by the HAM and the numerical integration (i.e. Runge-Kutta) method. It is shown that the analytical solutions of the HAM agree well with the numerical integration solutions, even if time t progresses to a certain large domain in the time history responses.