Experimental Identification of Nonlinear Continuous Vibratory Systems Using Nonlinear Principal Component Analysis

This paper presents a new experimental identification technique for nonlinear continuous vibratory systems. The governing equations of motion of a nonlinear continuous system are described by a set of nonlinear partial differential equations and boundary conditions. Determining both of them simultaneously is a quite difficult task. Thus, one has to discretize the governing equations of motion, and reduce the order of the equations as much as possible. In analysis of nonlinear vibratory systems, it is known that one can reduce the order of the system by using the nonlinear normal modes preserving the effect of the nonlinearity accurately. The nonlinear normal modes are description of motion as nonlinear functions of the coordinates for analysis. In identification, if one can express the data as nonlinear functions of the coordinates for identification, it is expected that accurate mathematical model with minimum degrees of freedom can be determined. Based on this idea, this paper proposes an identification technique which uses nonlinear principal component analysis by a neural network. Applicability of the proposed technique is confirmed by numerical simulation.