AN EXPERIMENTAL STUDY ON THE OUT-OF-PLANE MOTION UNDER THE EXTERNAL PRIMARY RESONANCE IN STRINGS
Strings were resonated in the neighborhood of the natural frequencies by external excitation. The phenomena of the out-of-plane motion due to the coupling effect of the non-linear stiffness in strings has been theoretically clarified by using the equations of motion which are the non-linear partial differential equations. In this study, we consider the string which is fixed at one upper end and external excited harmonic periodically at the other lower end. We show the equations of motion considering the characteristic of geometrical cubic non-linear restoring force under the external excitation in the string, and analyze theoretically the vibrational mechanism of the out-of-plane motion with method of the multiple scales to find out the equilibrium states and their stabilities from the amplitude equations. Finally, we compare the experimental results and the theoretical ones.