Abstract
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 while preserving the effect of the nonlinearity accurately. In identification it is expected that an accurate mathematical model with minimum degree of freedom can be determined if one can express the response as nonlinear functions of the coordinates for identification. Based on this idea, in a previous report the authors proposed an identification technique which uses nonlinear principal component analysis by a neural network. In this report, procedure to apply the identified result to structural modification is presented. It is shown via numerical example that when the structural modification is not so large, response prediction of the modified system with enough accuracy is possible.
