String vibrations having non-ideal boundary conditions

In this study, nonlinear vibrations of an axially moving string are investigated. There is a non-ideal support between the opposite sides which lets small displacements. Nonlinear equations of motion and boundary conditions are derived using Hamilton?s Principle. Equations of motion and boundary conditions are converted to nondimensional form. Thus equations become independent from geometry and material properties. Method of Multiple Scales, a perturbation technique, is used. A harmonically varying velocity function is chosen for modelling the axial movement. String as a coutinuous medium is investigated in two regions. Vibrations are investigated for three different cases of the excitation frequency W. Stability analysis is done for those three cases and stability boundaries are determined for principle paremetric resonance case. Thus, differences between ideal and non-ideal boundary conditions are investigated.