Identification and quantification of nonlinear stiffness and nonlinear damping in resonant circuits

This paper presents a study of nonlinear vibrating mechanical structures whose resonances have nonlinearities due to stiffness and/or damping. A method is presented to detect the presence of nonlinear distortions qualitatively and quantitatively. Basically, a device under test is configured as a second-order, single-input–single-output closed-loop feedback system where static nonlinearities are confined to the feedback path, and the dynamic linear part is modeled as the forward gain. The system is excited by a random phase multisine, which allows for the modeling of the linear part by its frequency response function, thus facilitating the characterization of the nonlinear part. The identification is formulated in a linear-in-parameters framework, using input and output regressors. A good agreement between the estimated data and the measurements indicates the presence of nonlinearities due to stiffness and damping with distinguishable levels.