Alternating frequency/coefficient (AFC) technique in the trigonometric collocation method

Abstract

The trigonometric collocation method is extended to non-linear systems containing convolution terms. A complete solution procedure is developed by reformulating the Alternating Frequency/Coefficient technique in conjunction with the trigonometric collocation method. Numerical results show that the procedure is computationally more efficient for large non-linear systems as compared to the harmonic balance method. In addition, compared with the conventional trigonometric collocation method, the new procedure is more effective in dealing with complex non-linear phenomena, especially in the vicinity of a bifurcation point.