Nonlinear forced vibration and stability analysis of nonlinear systems combining the IHB method and the AFT method

The incremental harmonic balance (IHB) method is a very powerful tool for analyzing nonlinear forced vibrations in structures subjected to periodic forces. In this paper, a methodology is proposed to interpret the stability of the calculated solutions and the nonlinear vibrations of nonlinear systems by combining the IHB method and the Alternating Frequency/Time (AFT) method. The main purpose of combining the IHB method and the AFT method is to analyze the nonlinear vibration of systems with complex nonlinearities. For the mass matrix, damping matrix, and linear stiffness matrix, the Galerkin procedure is performed according to the classical IHB method. The nonlinear force matrix and its derivative matrix are calculated in the time domain and transformed into the frequency domain by Fourier transform. By multiplying these matrices with a transformation matrix, they are transformed into matrices that can be used in the IHB method. Three example problems are proposed to prove the effectiveness of the suggested method and the results compared with the results calculated using numerical integration (NI) and the results presented in previous literature. The results are very close. The proposed method can analyze nonlinear vibrations of systems with complex nonlinearities as well as geometric nonlinearities. (C) 2022 Elsevier Ltd. All rights reserved.

Automated summary

The paper proposes a methodology that combines the incremental harmonic balance (IHB) method and the Alternating Frequency/Time (AFT) method for interpreting the stability of solutions and nonlinear vibrations in nonlinear systems. By using a transformation matrix, the calculated nonlinear force matrix and its derivative matrix are transformed into matrices that can be used in the IHB method. The effectiveness of the proposed method is demonstrated through three example problems.