Nonlinear Response of a Taut String to Longitudinal and Transverse End Excitation

The nonlinear response of a taut string to an end excitation with components both parallel and transverse to its axis is theoretically and experimentally studied. A model for the transverse vibration of the string is developed by neglecting its longitudinal inertia. The method of multiple scales is applied directly to the governing partial-differential equations and boundary conditions. A continuation method is then employed to determine the constant amplitude and phase solutions and their stability. Resonant responses are predicted to occur simultaneously in as many as three modes. An experimental study is conducted and the results are found to be in good agreement with the theory.