Abstract
A spatial string model incorporating a nonlinear (and non-conservative) material law is proposed using finite deformation continuum mechanics. The influence of material nonlinearities on the string’s dynamic response to excitation near a transverse natural frequency is shown to be small due to their appearance at high orders only. Material nonlinearities appear at low order in the equations for excitation near a longitudinal natural frequency and a solution for this case is developed by applying the method of multiple scales directly to the partial differential equations. An example string is considered to explore the influence of material nonlinearities on the dynamic response. Rich modal content is found, which can not be predicted by simpler models. Additionally, the material nonlinearities are shown to exert their greatest, influence away from resonance, where they serve to limit the response amplitudes.
