Jump-based estimation for nonlinear stiffness and damping parameters

To overcome the limitation that only stiffness nonlinearity can be estimated via jump frequencies, this work introduces jump amplitudes as a supplement condition in the estimation of both stiffness and damping nonlinearities. An estimation method is proposed for a single-degree-of-freedom system containing both stiffness and damping nonlinearities. The idea may be applied to other nonlinear systems. The method is based on the measurements of both jump frequencies and jump amplitudes of the system subject to swept-sine excitations respectively in frequency and in amplitude. The experimental data yield frequency response curves at a fixed excitation amplitude and amplitude response curves at a fixed frequency. Based on the measured jump frequencies and jump amplitudes of the displacements, the system parameters can be determined by the method of harmonic balance. A numerical example is presented to demonstrate the application of the proposed approach and to check approximate explicit analytical expressions of the parameter estimation. To validate the effectiveness of the proposed approach, an experiment is performed on a vibration isolator with strongly nonlinear stiffness and damping. The estimation results show that the proposed method can estimate the stiffness and the damping parameters of the system with strong nonlinearities. Hence exploiting the knowledge about nonlinear jump phenomena is a promising approach to parameter estimations.