Experimental nonlinear identification of a single structural mode

We describe a procedure for the identification of the nonlinear parameters of a single mode of a structure possessing quadratic and cubic geometric and inertia nonlinearities and linear and quadratic damping. We use this procedure to identify the parameters of the first mode of a portal frame consisting of three beams and two masses. The generalized coordinate of this mode is modeled by a second-order ordinary-differential equation possessing quadratic and cubic geometric and inertia nonlinearities, linear viscous and quadratic damping (airflow drag), and parametric and external excitation terms. The linear natural frequency and damping coefficient are estimated using linear tests. Then, the structure is excited by a harmonic force having a frequency that is approximately twice the natural frequency of the first mode, thereby producing a combination of a principal parametric resonance and a subharmonic resonance of order one-half. We use the method of multiple scales to determine a second-order uniform expansion of the model equation and hence the frame response to such an excitation. We estimate the nonlinear parameters by regressive fits between the theoretically obtained response relations and the experimental results. We report deviations and agreements between model and experiment.