Nonlinear vibrations of a string subjected to periodic excitation

Many papers studying the internal resonances in the string have been published. But most of them concern the internal resonances produced by a harmonic excitation. The characteristics of internal resonances produced by a periodic force may differ from the above. This report treats the internal resonances produced by an external force consisting of the fundamental and the third order harmonic components. The frequency of the fundamental component is supposed to be near to the natural frequency of the first mode, and hence the frequency of the third order harmonic component is near to the natural frequency of the third mode simultaneously. For this problem we conduct theoretical and experimental analysis, and show that many patterns of vibrations in which different modes are dominant can occur.