The identification of external forces for a nonlinear vibration system in frequency domain

Based on the perspective of nonlinearities as internal feedback forces, the external force identification model for the nonlinear vibration system is established in the frequency domain. In general, the accuracy of proposed technique is often limited by the noise in the measured structural responses and the inversion of the ill-conditioned linear frequency response functions matrix. Hence, the force identification problem always changes to be an ill-posed problem, and in order to obtain the stable solution, the ordinary least square method, combining with a regularization technique, is used in this paper. Finally, in order to verify the practicality and accuracy of the proposed method, a numerical example and experimental application are used. The results show that it is feasible to apply the proposed method to identify the external force for a nonlinear vibration system.