chaotic motion and its control for a non-planar non-linear cantilever beam with parametric excitation

in this paper, chaotic motion analysis and its control for a non-planar non-linear cantilever beam with axial and lateral parametric excitation in the free end is accomplished. this is a new method for control of chaotic motion of a non-linear planar beam. in this survey, internal resonance of the beam is 2:1 and the initial resonance is in the outside of plane and it is assumed a sub-resonance for inner plane. the beam is modeled with lagrange method. then, multi comparison method is used for system transformation of parametric and external excitation to the averaged equation where the constant load applied to them. finally, with the usage of numerical simulation, an open loop control is designed for chaotic motion of non-planar cantilever beam which excited in the free end to reduce the beam vibration in one axis. the results are presented in the curves to show the limit of stability.