Nonlinear damped forced oscillators with quadratic-biquadratic nonlinearities

A modified harmonic balance method (MHBM) has been extended for solving strongly nonlinear damped forced oscillators with quadratic-biquadratic nonlinearities. Depending on the parameter values and initial conditions, its behavior is quite complex. The proposed method allows us to expand some Fourier coefficients in a power series, which helps to provide analytical solutions. Traditional perturbation methods (e.g., averaging, Krylov-Bogoliubov-Mitropolskii (KBM), and multiple time scale) and the classical harmonic balance method are often inadequate for obtaining similar approximate solutions. The solutions obtained by the proposed method nicely coincide with corresponding numerical solutions.