A method for simultaneous identification of the full nonlinear damping and the phase shift and amplitude of the external harmonic excitation in a forced nonlinear oscillator

We propose a new general method that is able to clarify the simultaneous identification of the full nonlinear damping characteristics as well as the phase shift and amplitude of the external harmonic excitation in a forced nonlinear single degree system. The method is the non-parametric identification based on the concept of zero-crossings regarding the system responses. It involves an integral equation of the first kind, resulting in the lack of stability properties. The difficulty of instability is overcome by the stabilization technique. The workability of the proposed method is demonstrated through a numerical experiment consisting of a highly nonlinear system.