System identification of a beam with frictional contact

The nonlinear system becomes an area with numerous investigations over the past decades. The conventional modal analysis could not be  applied on nonlinear continuous system which makes it impossible to construct the reduced order models and obtain system response based on limited number of measurement points. Nonlinear normal modes provide a useful tool for extending modal analysis to nonlinear systems but the extraction of nonlinear normal modes is cumbersome. In this research by neglecting the damping effect on response shape, the nonlinear joint in frictional beam is replaced by 3 order nonlinear spring. The equation of motion is solved using the method of multiple scales up to third super harmony which are neglected in most system identification practices. It is shown in an experimental test set-up, the general form of solution can regenerate observed response of any point and more important similar to linear system, the single mode would be sufficient in analysis when excitation frequency is close to resonant frequency.