Non-parametric simultaneous identification of both the nonlinear damping and restoring characteristics of nonlinear systems whose dampings depend on velocity alone

This paper presents a general method, which is aimed at identifying both the nonlinear damping and restoring characteristics of nonlinear oscillation systems in which the nonlinear damping is characterized as a function of velocity alone. The method developed for this simultaneous identification involves the non-parametric identification of nonlinear systems. Both system displacement and velocity responses are required for its implementation. However, the numerical approach to this method results in the instability of the numerical solutions, which also means that the solutions identified lack of stability properties. This difficulty is solved by employing a stabilization technique (or regularization). Although the method presented herein is built on the basis of the measurement of the system displacement and velocity responses, a conceptual systematic procedure is also proposed to describe how the system’s acceleration response can be used for simultaneous identification. Finally, an example involving a highly nonlinear system is presented to demonstrate the proposed method’s workability for simultaneous nonlinear system identification.