Modified residue harmonic balance solution for coupled integrable dispersionless equations with disturbance terms

This is a supplementary study of the solution method previously proposed by the author (Lee, 2017; Rahman and Lee, 2017). The proposed method is used for solving three-coupled integrable dispersionless equations with disturbance terms. It has only been adopted for solving (1) a nonlinear beam problem, and (2) a nonlinear vibro-acoustic problem. In the solution process, the three-coupled nonlinear equations can be transformed into only one Duffing equation. The higher-level nonlinear solutions, which were ignored in the previous method, can be generated using the proposed approach. Hence, in each step in the solution, only one independent nonlinear algebraic equation need be solved. As in the previous method, the proposed method has the advantage that the periodic solutions are represented by Fourier functions rather than the tedious implicit functions. The solutions from the proposed method agree reasonably well with those obtained from the classical harmonic balance method.