An indirect harmonic balance method based on frequency response functions simplification for periodical response analysis of local nonlinearity systems

Abstract

The majority of the nonlinear factors introduced into engineering tend to exhibit locality rather than globality. This paper proposed a novel indirect-HBM (indirect Harmonic Balance Method) based on the perspective of local nonlinearity. The excellent performance of this method stems from its HE (Harmonic Equation). The indirect-HE (HEs of the Indirect-HBM) were composed of the FRF (Frequency Response Function) directly and it can be subdivided into Key-HEs and Aug-HEs (Augmented HE). Here, the Key-HE serves efficient computation, while Aug-HE meets various engineering needs. In this research, a FEM(Finite Element Medel) with one cube nonlinear and an infinite dimension rotor system with gap nonlinearity was employed to investigate the computational performance. First, the accuracy of indirect-HBM was verified by the numerical solution based on the 32-DOF FEM. Then, compared with the classical HBM, its computational efficiency can not be constrained by DOFs. Finally, It was applied in an infinite-dimension nonlinear rotor system, which implemented a solution based on PDE rather than ODE. The numerical solutions based on different FEMs prove that the indirect-HBM has the fidelity of the dynamic model. From the perspective of local nonlinearity, the indirect-HBM offers a novel solution approach and excellent computational performance.