A Parametric Identification Technique for Single-Degree-of-Freedom Weakly Nonlinear Systems with Cubic Nonlinearities

We present a procedure for the identification of parameters describing a single-mode response of a structure possessing cubic geometric and inertia nonlinearities and linear (viscous) and quadratic damping (air drag). We use this procedure to identify the parameters describing the third mode of a cantilever beam. The beam is externally excited by a harmonic force having a frequency close to the beam's third natural frequency. We use the method of multiple scales to determine a first-order uniform expansion of the model equation and hence the beam response to such an excitation. We estimate the parameters based on the experimental frequency-response results and later use these values in the theoretical model. We then compare the model results with the experimental results. For the fourth mode, a comparison is also made between the results obtained using the proposed estimation technique with those obtained by the frequency-response curve-fitting method. We report on deviations and agreements between model and experimental results.