An attenuation signal-based identification approach for parameters in weak nonlinear systems with asymmetry

This paper introduces a method to identify the parameters in a weak nonlinear vibration system. Based on the existed backbone curve identification method which can identify the parameters in weak nonlinear symmetric systems, method in the present paper extends the application of 'backbone curve' method to nonlinear systems with asymmetry. Based on the introducing of offset term caused by the asymmetry, this method can increase the number of identification equations to broaden its application. Meanwhile, the data obtained from the displacement attenuation signal offer valuable information of system nonlinearity in this method. So we can identify all the parameters of system only from its displacement attenuation signal. As an application, we design a vertical cantilever beam with initial deflection and tip mass as an experimental object with asymmetric structure. The displacement data of the top of beam are acquired by a laser vibrometer. The provided method is applied to identify all nonlinear parameters in the model of the nonlinear cantilever beam. Then, the validity and accuracy of method can be evaluated by the comparison between theoretical parameters and identified parameters of beam model.