Novel identification technique through the coordinate transform of smooth nonlinear vibrating systems

This study presents a unique nonlinear frequency response NLFR extraction method introduced for smooth nonlinear vibrating systems. The proposed methodology is built on the geometrical representation of the harmonic balance solution for the undamped cubic Duffing oscillator. It is demonstrated that a curvilinear coordinate transform (CCT), defined by the so-called backbone curve (BBC) of the nonlinear normal mode (NNM), allows the comparison of linear and nonlinear systems in its atomic representation. Then, a unique way of extracting unstable periodic orbits is shown based on the CCT method.