Experimental Nonlinear Model Identification of a Highly Nonlinear Resonator

In this work, two model identification methods are used to estimate the nonlinear large deformation behavior of a nonlinear resonator in the time and frequency domains. A doubly clamped beam with a slender geometry carrying a central intraspan mass when subject to a transverse excitation is used as the highly nonlinear resonator. A nonlinear Duffing equation has been used to represent the system for which the main source of nonlinearity arises from large midplane stretching. The first model identification technique uses the free vibration of the system and the Hilbert transform (HT) to identify a nonlinear force-displacement relationship in the large deformation region. The second method uses the frequency response of the system at various base accelerations to relate the maximum resonance frequency to the nonlinear parameter arising from the centerline extensibility. Experiments were conducted using the doubly clamped slender beam and an electrodynamic shaker to identify the model parameters of the system using both of the identification techniques. It was found that both methods produced near identical model parameters; an excellent agreement between theory and experiments was obtained using either of the identification techniques. This follows that two different model identification techniques in the time and frequency domains can be employed to accurately predict the nonlinear response of a highly nonlinear resonator.