A Generic Pre-Processing Technique of IHB Method for Continuum System to Improve Calculation Efficiency

Modal discretization is commonly applied for dynamic analysis of non-linear continuum system. Considering the possible coupling effect between modes is necessary to obtain accurate results. In this case, the system may become increasingly complex, as the number of adopted modes can be a lot. Such complexity will lead to the difficulty of solution finding. This paper proposes a generic technique to simplify the governing functions by making non-linear stiffness matrix symmetric. The symmetric non-linear stiffness matrix is constructed by utilizing the mode shape vectors. The proposed procedure can theoretically guarantee non-linear stiffness matrix symmetric. The incremental harmonic balance (IHB) method is served as the main tool for finding solutions of systems. Dynamic analysis of axially moving beam and generalized suspension bridge are presented in this study for illustration. Results proved that the neighboring modes are critical during the resonance of target mode, which suggests the necessity of including sufficient modes for non-linear dynamic analysis. By applying the proposed technique, it is found that calculating time of IHB method can greatly shortened, especially for the case included modes becomes large. Results show that the time consumption with using the proposed method can be half of that not using it, when more than 5 modes are considered in the calculation.