An efficient extended IHB method for non-linear dynamic analysis with multi-frequency harmonic excitations using an auto adapted truncation technique

Demand on the analysis of a nonlinear system under multi-frequency harmonic excitations is commonly encountered in an engineering field, which requires a feasible analysis technique. The existing incremental harmonic balance method, however, shows an apparent deficiency in the calculation efficiency, due to the inappropriate rule of selecting frequency components of solutions. A highly efficient extended incremental harmonic balance extended IHB method is developed to tackle this problem. Firstly, multiple time scales are introduced to express the solutions. Secondly, through detailed examination of the response Fourier spectrum, an auto adapted truncation technique of Fourier series is developed for selection of necessary harmonic terms of solutions. The adopted harmonic terms vary in every round of solution tracing, according to the amplitudes of the harmonic terms of interest. The feasibility of the proposed method is illustrated through three different examples. The accuracy of the method is verified by comparing the obtained results with that those from the Runge-Kutta method. The efficiency of the proposed algorithm is compared with that of the algorithm of the Pusenjak-Oblak method. It is shown that the proposed method can dramatically reduce the number of harmonic terms, as it only needs a maximum of one-fifth of harmonic terms of the existing method. Such results suggest that the proposed method has a strong advantage in the calculation efficiency for analyzing a nonlinear system under multi-frequency harmonic excitations.